What is the difference between .45 cal and .44-40 cal?

difference is bullet size. Note the '45' is a larger number then '44'. So, can't shoot the 44 in a 45 nor can you shoot the 44 in a 45, the 44 is too small. It's merely SIZE...............( the cartridge cases also make a difference in that they also differ in size) 45 diameter is .451 or .452 44 diameter is .429