They both use the .45ACP.
It is never a bad question. There is many varieties of numerous calibers, some of which many of us take for granted, but could be quite confusing to someone first researching things.
No wrong question, it sure is better to ask even if just to be sure, that to remain ignorant out of fear of asking a logical question.
There is many rounds that can be confusing. Take 9mm for example. There is numerous 9mm rounds, however we usualy assume people are talking about the 9x19. There is in fact several dozen different 9mm rounds, some called by metric numbers, some of the same or near diameter given in inch calibers.
You can also learn odd things. Like some older rounds have a modern equivalent that is actualy a slightly different diameter than the traditional round. The .45 Colt, often called the .45 "long colt" to not confuse it with other rounds was traditionaly a .454 diameter bullet. However many modern guns are actualy chambered smaller, from .451-.453 since the jacketed rounds are .451, the same as the 45ACP. That means one actualy chambered for firing the old rounds of solid lead rounds exclusively would be quite innacurate firing the smaller .451 rounds that often come from the factory. It would have too much room, not engage the rifling on a .454 barrel well, and have a lot of the pressure slip around the bullet in a random way letting the bullet fly in a slightly random direction off center each time.
So there is different .45 Colt chamberings, and different .45 Colt bullets even though they are all .45 Colt. All will work, but some will work better for a particular gun.
Most modern guns are chambered to work best with the modern factory rounds. However now that cowboy action shooting is popular some new guns are chambered differently.
Many into cowboy action shooting learn that the hard way and are just a horrible shot until they learn the "secret", to use bullets of the correct bore diameter with those weak loadings.
That is something many take a long time to learn because they don't want to seem like they don't know something and simply don't ask questions that lead to the right unexpected answers. Pride can leave one ignorant.
Yet they are all .45 Colt. Many also call ".45 Colt" ".45 Long Colt" because technicaly .45ACP (Automatic Colt Pistol) is A .45 colt as well, it is just not THE .45 Colt. So it could be quite easy for someone that did not know better to make some sort of mistake in communication. To add some margin of error people say .45 "Long Colt", because there is no way to possibly confuse the two, because there is only one round anyone would call .45 "Long Colt".
Another interesting trivia. The .45ACP Thompson Submachinegun has a barrel length that is the perfect length for the round to gain the maximum amount of velocity.
A 16" barrel actualy loses power over a 10.5 inch barrel. The round peaks with a standard loading between 10 and 11 inches.