ANNAPOLIS -- Maryland Lt. Gov. Melvin A. Steinberg sent a subtle message last week in a debate with his Republican counterpart, but not one intended for the opposition.

Just by showing up at a campaign event with Lois B. Shepard, Steinberg was straying from Gov. William Donald Schaefer's official campaign strategy of ignoring the competition at all costs. In so doing, Schaefer supporters thought, Steinberg made Schaefer look bad for not debating his own challenger.

But for Steinberg, a 25-year Maryland political veteran with undisguised ambitions to run for governor himself in 1994, showing independence is that important right now.

"Maybe it put the governor in a less than satisfying situation . . . but he decided to do it as his way of showing his feelings about certain subjects," said Del. Richard Rynd (D-Baltimore County), a close Steinberg ally.

Steinberg's future, associates concede, remains inextricably linked to Schaefer. However, with polls now showing the Schaefer-Steinberg ticket apparently heading for victory Nov. 6, Steinberg has begun seeking subtle ways to distance himself from Schaefer in the next four years, Steinberg allies say.

The intra-ticket flap over debating is only the latest disagreement as Schaefer, a former longtime Baltimore mayor, also puts some distance between himself and Steinberg. The lieutenant governor's name and likeness are absent or an afterthought in much of the campaign advertising.

Soon after the September primary, Steinberg openly complained that the campaign had appropriated his name without permission by forming a second campaign committee, Citizens for Steinberg. Schaefer's campaign manager wanted to use the committee to take contributions from donors who had already given the maximum to Schaefer's other committee. But Steinberg had other ideas.

Because Schaefer already enjoyed a 20-to-1 fund-raising advantage over GOP candidate William S. Shepard, Steinberg said that amassing even more money for the ticket could be viewed as "arrogance" or "overkill."

Among some Schaefer allies, Steinberg's protest was viewed as camouflage for the lieutenant governor's desire to reserve the same financial sources for the next gubernatorial campaign.

"The campaign people just couldn't understand that I have to be a separate personality," Steinberg said in an interview this week.

Campaign managers subsequently decided not to use the separate committee and found another approach, but the incident brought into sharp focus long-simmering differences between Steinberg and the strong-willed governor, and it highlighted the difficulty any ambitious lieutenant governor must face eventually.

"It's very much an evolving relationship between them, subject to the natural ebbs and flows of the jobs," said Alan Rifkin, a lobbyist who has worked for both Steinberg and Schaefer.

One political analyst, familiar with the volatile governor, put it more starkly: "In Schaefer's galaxy, there's only room for one planet, and that's him."

People who talk about a rift between the two Democratic leaders are seeing "ghosts," replied Paul E. Schurick, Schaefer's press secretary. Others blame warring staffs and potential 1994 rivals with spreading rumors of a Schaefer-Steinberg split.

Schaefer aides point out, correctly, that during the last four years the governor has given Steinberg broader authority and visibility -- putting the former state Senate president in charge of his legislative proposals -- than any other lieutenant governor since the office was reestablished in 1970. Steinberg, in return, has been credited with pushing through some of Schaefer's most cherished programs, including the Baltimore stadium, a trolley line and restructuring of higher education.

But Senate President Thomas V. Mike Miller Jr. (D-Prince George's), a lieutenant when Steinberg was Senate president but now a possible contender himself for the gubernatorial nomination in four years, said there are "obvious strains in their relationship."

In many ways, the Schaefer-Steinberg team is a marriage of political convenience between vastly different mates. Schaefer is suspicious of compromise and will bully for verbatim approval of his programs, never forgetting a defeat. Steinberg, on the other hand, grew to politicial maturity in the General Assembly and emerged a master of back-slapping and concensus-building for whom accommodation is second nature.

Given their disagreements during the campaign, some lawmakers predict that Schaefer will shut him out of decision-making if the team is reelected next month. "Having kept Steinberg in the background for four years, Schaefer resents him now stepping out on his own now," one legislator said.

Steinberg, 57, a Baltimore County lawyer and investor, says that reports of differences between him and Schaefer are overblown and don't extend to government policies.

"It's important that the lieutenant governor work in concert with the governor, but it's an independent constitutional office," Steinberg said.

In fact, the Maryland Constitution makes the governor and lieutenant governor run as a team but gives the lieutenant governor only those powers delegated by the governor. The office has not been a political steppingstone, either. None of the three other lieutenant governors since 1970 has been elected governor.

Several leading Democrats said Steinberg is beginning to test the limits of his office to see whether he can position himself as a loyal soldier for Schaefer and an independent leader who is the logical heir.

Steinberg acknowledged that he can't have it both ways -- winning credit for the accomplishments of an administration while avoiding blame for its shortcomings.

"A lieutenant governor cannot escape . . . but he can dilute the negatives by being recognized as an individual personality," Steinberg said.

Said one observer of the State House, "It's very astute on his part, but whether the governor lets him get away with it is another matter."