WITH THE APPOINTMENT of a special counsel, the Carter administration has promised a definitive reply to all the questions about the president's family business. Those questions can be summarized by asking whether the mishandling of the money at the peanut warehouse has any similarity to the Watergate scandals. So far, there's no evidence of it -- no evidence that President Carter himself had anything to do with the mishandled funds. Watergate was, after all, not only the original crimes of the bugging and the break-ins but also the subsequent crimes, directly involving a president, of the cover-up.

But the special counsel, Paul J. Curran, is going to have to deal explicitly with the charges that the illegalities at the warehouse were only part of a larger and darker design to funnel money from Bert Lance's bank to the Carter presidential campaign during the 1976 primaries. As lawyers say, Mr. Curran is going to have to prove a negative. It won't be enough for him simply to say that he can't find proof of wrongdoing. He will have to go through the wildly disheveled finances of the warehouse and account for every nickel that passed through them.

The affairs of the Carter warehouse have become a bublic issue as a result of the federal grand jury investigation into Bert Lance's management of the National Bank of Georgia. The investigators discovered that the Carter peanut warehouse was the bank's largest customer, and that the bank had made unusual and apparently illegal concessions to it. Specifically, it had held a large number of kited checks written by Billy Carter.

When Jimmy Carter embarked on his long run for the presidency, Billy became the manager of the family's peanut warehouse business. It seems that, over the succeeding years, he followed a course of increasingly hard drinking, heavy spending and reckless bookkeeping. In the spring of 1976, the warehouse accumulated an illegal deficit of $500,000, according to a former employee, by selling off peanuts that were being held as collateral for loans from the National Bank of Georgia. When the employee quit in the summer of 1976 and notified the bonding company, the matter was setted quietly. The method is not quite clear, but it seems that some of that deficit was transferred to the bank by checks that Billy Carter wrote against insufficient deposits. In 1976-77, drought damaged the local peanut crop, and Billy Carter's troubles deepened. His erratic behavior came to public notice last January, when he emerged briefly as a guide and apologist for a delegation of visiting Libyans. Shortly afterward, some of the grand jury's discoveries began to leak out of Atlanta. By February, Charles Kirbo, as trustee for the major partner, President Carter, was looking for a buyer for the warehouse.

Is there anything more to it, than that -- anything more than a sorry story of a spendthrift younger brother and a bank that bent rules for certain wellconnected customers? We doube it, but we cannot make a flat statement. That requires the exhaustive pursuit of answers that the special counsel is now undertaking.

President Carter's adversaries have made much of the point that Mr. Curran is to be only a special counsel rather than a special prosecutor. The Carter administration first got itself into an absurd dispute over the legal limits on Mr. Curran's authority. Then, wisely, it gave in and conceded to him the same powwisely, it gave in and conceded to him the same powers that the former special prosecutor had -- but not that title.

The quarrel over nomenclature is not so frivolous as it might at first seem. It concerns the language of scandal and the power of word association. President Nixon was, unarguably, corrupt. A good many people once close to him feel a deep interest in suggesting that all presidents must be, to one degree or another, similarly touched by corruption. The familiar refrain of the Nixon defense was: "Everybody does it." The very phrase "special prosecutor" evokes the Nixon-Watergate period. That is why the Republicans are attempting to attach it to the Carter administration -- and why the Carter administration is struggling, although not very adroitly, to avoid it.

If Mr. Curran finds nothing that touches the president, there will be charges, also drawn from the Watergate vocabulary, of cover-up; in fact, that cry has already begun. That is another reason for Mr. Curran to do his work with compelling thoronghness and skill.