.45 Colt is probably the first cartridge invented from your list there. It's a revolver cartridge, with a rim, and will not fit in a semi-auto not designed for the round.
.45 ACP (Automatic Colt Pistol) is the pretty standard ".45" cartridge for .45-caliber semi-autos. This cartridge is "rimless" meaning the rim that the extractor catches on is flush with the sides of the case. A case drawn of, say, the edge of a table will not catch.
.45 GAP (Glock Automatic Pistol) is essentially a .45 ACP shortened so Glock could shorten the grips on their .45-caliber pistols making them fit some peoples' hands better.
I'm not real sure about the .45 Auto Rim or .45 Super, can't help you there.
I believe there's also a .45 Scholfield, and we don't need to get into .45-70, .45-90, etc.
If you're looking for ammo for a Taurus Mil Pro I believe that you should look for .45 ACP. There should be some markings dictating specific caliber somewhere on the firearm, or the packaging it came in. In my experience, if the slide/barrel/frame are stamped ".45 Auto" it's referring to .45 ACP.