One December day last year, officials of the Dreyfus Corp., a $10 billion Wall Street mutual fund, crossed the Hudson River to East Orange, N.J., and paid $2.7 million for tiny Lincoln State Bank.

Federal law is supposed to separate the banking and securities businesses, but Dreyfus had a ready answer when the Federal Reserve Board objected to its move into banking.

Ducking nimbly through a loophole in federal law, Dreyfus declared that Lincoln State was a "non-bank" because it had stopped offering certain banking services.

That was good enough for the Federal Deposit Insurance Corp., which promptly approved the purchase. But the Federal Reserve objected that Lincoln State was "a non-bank bank." It called on Congress to settle the dispute between the two agencies.

Lincoln State "non-bank bank" is a symbol of the upheaval in the money business, as banks and securities firms move into each other's service areas.

With federal regulators unable to agree even on what a bank is, Congress, the financial industry and consumers face some difficult questions as they enter the age of financial supermarkets:

* Can home town banks and traditional financial relationships survive competition from nationwide financial supermarkets?

* Will adequate funds be available for mortgages, consumer loans and small businesses as deregulation opens up more lucrative business opportunities?

* Can half a dozen separate regulatory agencies adequately oversee financial institutions that are all moving into each others' businesses?

Will consumers benefit from the proliferation of new borrowing and investing opportunities or will they suffer from a confusing and costly array of services they don't need or want?

* Will the nation's financial system be strengthened by these changes or exposed to the risks that spawned financial regulation after the Great Depression?

The banking revolution has left federal regulators "panting to catch up," says Treasury Secretary Donald T. Regan, an advocate of fast deregulation. "Congress should catch up with what's going on in the world. You can't have laissez-faire because you're dealing with people and their money. You can't expose them to too much risk."

If, on the one hand, bank deregulation quickens, the banks may lose their way in uncharted waters. On the other, if the government continues to delay bank deregulation, other types of financial institutions will continue to invent new products that are not supervised by the government.

"It's this 'damned if you do, damned if you don't' dilemma that is on Washington's mind," said Comptroller of the Currency C. T. Conover. "And either way, the level of risk in the financial services system increases."

There is nothing close to a consensus on whether to tear down the existing legal structure and build anew or to patch the old one. An effort to begin catching up with the revolution by sorting out the issues will begin tomorrow when the Senate Banking Committee begins a series of hearings on financial regulation. But the drafting of any major federal banking legislation is expected to take at least two years, according to key members of Congress.

Committee Chairman Jake Garn (R-Utah) does not expect the hearings to lead to massive deregulation like that now occurring in transportation and broadcasting. "The political reality is changes, not repeal," he said.

Yet Rep. Fernand J. St Germain (D-R.I.), who chairs the House Banking Committee, sees no pressing need for legislation in the near future, citing grass-roots opposition to change.

"We can't let these insured financial institutions go into all kinds of businesses because then we would have to ask our regulators to be pundits and to analyze their business investments. I think that's impossible," he said. "Many institutions will want to offer full services. The next thing you know, they'll have an obstetrician and pediatrician at one end, a funeral director at the other and financial services in between. Let's use a little common sense. Technology is great for institutions, but we must not lose sight of what's good for people. How many of them will use it?"

The strictest view of banking is held by the nation's central bankers. E. Gerald Corrigan, president of the Federal Reserve Bank of Minneapolis, recently declared that banks are "special" institutions because they serve a public purpose as the backup source of liquidity to all other institutions and are the "transmission belt" for monetary policy.

Corrigan suggests that any non-bank institution that offers checking accounts should be federally insured and should have to abide by the same rules that govern banks. The net effect of his proposals would be to retard many innovations in financial services.

"The public safety net federal insurance reflects a consensus that banking functions are essential to a healthy economy," Corrigan wrote. "Its presence also implies that banks have unique public responsibilities." As such, he continued, they should remain separate from other types of financial institutions like securities firms and insurance companies. "Subsidiary banking activities should not entail excessive risk of loss and should not impair the impartiality of the credit decision making process."

Much the same argument was once voiced about savings and loan associations: they deserved government protection because they "specialized" in housing. Partly as a result, that industry was decimated by inflation whereas other financial institutions fared better. With S&Ls free to pay higher rates to depositors and to compete with banks for commercial loan business, critics raise the specter of scarce and expensive mortgage money. That does not appear to be happening at present.

Economist Henry Kaufman, the guru of Wall Street, believes that deregulation hampers the central bank in its efforts to control monetary policy. Previously, when banks ran short of funds because they could not pay depositors above a certain rate, they stopped making loans. The resulting slowdown in the economy dampened inflation. Now that there is no limit on deposit rates, the banks just add their profit margin to the amount they pay for deposits and keep lending. The result is continued high interest rates, Kaufman contends.

Turn these views 180 degrees to get the philosophy of the free marketers. These include big banks and other financial industry giants, the Reagan administration and the banking regulators other than the independent Fed, plus get-the-government-off-our-backs groups like the conservative think tank, the Heritage Foundation.

The lexicon of the deregulators includes terms like market forces, opportunities, flexibility and responsibility. William M. Isaac, chairman of the Federal Deposit Insurance Corp., heads the drive away from absolute government protection for banks and toward the system of risks and rewards common to all industry. That makes sense, this theory holds, because banks henceforth will be increasingly engaged as well in other types of commerce like real estate investment and securities.

Rather than detailed federal regulation, Isaac favors public disclosure of banks' financial condition, which, he contends, would dissuade depositors from putting their money in shaky institutions. He would establish private insurance coverage for a portion of deposits over the $100,000 insured by the government. Isaac's argument is that private insurors would watch the banks more closely and charge higher rates than the government; therefore, banks would be less likely to take excessive risks.

Another variation on the theme would provide for differing rates of government insurance, depending on the soundness of the institution. Critics claim that unsound banks could not survive under a tiered system because their higher premiums would not allow them to compete effectively and the public might be inclined to boycott them.

Safety and soundness have traditionally been the cornerstones of the banking system. The deregulating regulators believe that market forces will cut down risk. At the same time they publicly admit that with increased opportunities, the freedom to succeed also means the freedom to fail.

The current bank examination process failed to prevent Penn Square National Bank in Oklahoma City from going under last year in one of the largest failures this country has ever witnessed. Now Baldwin-United Corp., one of the first "financial supermarkets"--a piano manufacturer that became a conglomerate of insurance, banking, mortgage banking, savings and loan and other investments--is in deep financial trouble.

Comptroller Conover, citing the enormous staff requirements that would be necessary to police banks in all their new activities, has stated that the country cannot afford a fail-safe banking system.

The congressional hearings opening tomorrow will focus on the basic federal laws that have governed banking for a half-century. Named after the legislators who wrote them, they are the Glass-Steagall Act of 1933 and the 1927 McFadden Act, and the Douglas Amendment to the Bank Holding Company Act of 1956. Glass-Steagall was created in the wake of the 1929 crash to halt the speculation by banks in the stock market. McFadden-Douglas bans branching across state lines by banks and bank holding companies.

Yet these laws are now being challenged everywhere in the country. The Washington area is a classic case. A few years back, a holding company that owned a group of smaller banks in the District, Virginia and Maryland decided to give all its banks the name First American; to launch joint marketing efforts and to set up a joint interstate teller machine system. The First American Banks in the three jurisdictions are still separate institutions, but that matters little to customers who enjoy many of the advantages of interstate banking.

Citibank recently announced the purchase of a small bank in South Dakota because that state's laws will permit Citibank to get into the insurance business, something federal laws prohibit.

Several states already have acted to update what reformers consider antiquated laws. The New England states recently approved a limited interstate branching experiment excluding New York banks. Delaware plans to give state-chartered banks more leeway to get into insurance, real estate, data processing and communications.

Despite his personal opposition to interstate banking, Sen. Garn concedes that "it is occurring in the marketplace and will continue to happen." He asks rhetorically, "Are we going to open our eyes and study it or hide from it and let it happen without any congressional input?"

Garn said he has no objections to letting banks and securities firms compete in each other's business, provided the change is properly structured, but says the country is not ready.

The Reagan administration advocates eliminating geographic restrictions on branching, saying in effect that they are not good for the consumer. "Although these prohibitions may reduce the concentration of financial resources on a national scale, they may also increase market concentration and lessen competition in local banking markets," the Council of Economic Advisors stated.

As for Glass-Steagall's barrier between banking and securities businesses, the administration study concludes: "It now makes no important contribution to the protection of the public against bank failure or undue concentrations of economic power. The financial and securities markets of today operate relatively unencumbered by unnecessary regulations, owing to deregulatory advances."

Secretary Regan favors a gradual approach toward ending cross-state and cross-industry prohibitions. He would like to see Congress allow interstate banking in natural marketing areas such as New York City, Connecticut and New Jersey. And he would ease restrictions against banks underwriting municipal revenue bonds and mutual funds through subsidiaries.

Small banks remain opposed to interstate banking because they fear being swallowed up by the giants. The securities and insurance industries have vowed to oppose changes in the law that would allow banks on their turf. But within the competing industries, there is sharp division over how far deregulation should go.

Joseph J. Pinola, chairman of First Interstate Bank, which has established the country's first bank franchise--selling its name and expertise to other banks--declared, "We're running as fast as we know how to get around Glass-Steagall. The longer it takes for us bankers to get into securities , the more the public will become accustomed to getting financial services from Sears and K-mart."

But John H. Gutfreund, managing partner of Salomon Brothers, says, "Glass-Steagall doesn't interest me that much; there is nothing I'd like to do in terms of the law that I can't do now."