T WO of the nation's most conservative Senators, Jesse Helms of North Carolina and Orrin G. Hatch of Utah, are locked in an unusual conflict over the abortion issue that has irritated the staffs of both Republicans. The two Senators strongly oppose abortion but are seeking wholly different means to outlaw it.

Behind this, some conservatives say, is a simmering dispute over which of the two men will actually lead the anti-abortion fight in the Senate. Mr. Helms is irritated at Mr. Hatch's opposition to a bill that specifies that ''the life of each human being starts at conception,'' thus giving fetuses rights under the Constitution. Mr. Hatch has said that he has ''serious constitutional reservations'' about the bill. He prefers instead a constitutional amendment authorizing Congress and individual states to regulate abortions.

For the past few months Administration aides as well as others on both sides of the issue have assumed that the ''conception'' bill, which was sponsored by Senator John P. East of North Carolina, a protege of Senator Helms, had run aground because of the opposition by Mr. Hatch and other conservatives. In fact Mr. Hatch, as chairman of the Subcommittee on the Constitution, is scheduled to start hearings on his own measure.

Suddenly Mr. Helms has taken the highly unusual procedural move of placing a ''new'' abortion bill, in fact the same one sponsored by Mr. East, on the Senate calendar, therefore circumventing the committee process. According to Senate conservatives, the move is designed to place a little pressure on the leadership to move on the abortion question and, perhaps more important, to steal a little thunder from Mr. Hatch, whose aides were described as ''a little bit peeved.''