As H&H shows, the .44s were Sharps' mainstay for a long time. I think that was what Jack Bean shot a hostile with at extreme long range.
Yet in or about 1880 they cataloged that they were making only .45s except on special order. Too bad they folded in 1881.
They offered a lot of different length .45s from .45-75 on the Government 2.1" case but with their typical paper patch bullet, through 2.4", 2.6", and 2 7/8" brass. Case length is definitive, there were different powder/bullet loads so the Winchester style designations are less informative. There is a lot of debate on the 3 1/4" case. I am in the school of thought that it was not a factory option but was only done as a rechamber and that not very often.
When the Brownings got around to making single shots with "the strong Sharps breechblock", the .40 was popular, usually the .40-70 Sharps Straight.
But Buffalo Bill's favorite Lucrezia Borgia was a "needle gun", a Trapdoor Springfield .50-70.