That is correct, the .32 colt short and .32 colt long are dimensionally the same as the .32 rimfire, Marlin shipped their 1891 lever guns with firing pins for the rimfire and the centerfire, both rounds were loaded with heeled bullets, just like the .22 and .32 rimfires. Colt came out with the .32 colt in 1875. A .32 smith and Wesson or as colt called it the .32 colt new police will not chamber in a .32 colt, it is too wide and the rim is a little bit bigger.
Winchester still loads factory ammo for the .32 colt short, they have one loading for it, it is an 80gr heeled lead round nose bullet. 32 colt long you have to reload for.