Hi Mike,
A "bullet" is the missile, or projectile only. A "cartridge" is the whole unit of assembled ammunition - case, powder, primer, and bullet. And "caliber" refers to the diameter of the projectile (bullet) or the approximate diameter of the bore of the gun. There is a lot of confusion with those three words - bullet, cartridge, and caliber. The confusion can sometimes overwhelm a newcomer, especially when you consider that at Walmart you can probably find at least 4 different types of .38 caliber cartridges - .380 ACP, .38 Super, .38 Special, and .357 Magnum. I'm not sure, but you might be able to find even more than that. And to make the confusion even worse, not a darn one of the cartridges I named are a true .38 caliber - they're actually only .35 caliber - that's why a .38 Special will work in a .357 Magnum.
You said you understand your "Colt 45." If you'll look at Walmart for cartridges to use in your Colt 45, you'll probably find at least 3 types of .45 caliber handgun cartridges. One will be the .45 ACP (Automatic Colt Pistol), another the .45 Colt, and the third will be the .454 Casull. I'm not sure which cartridge is right for your handgun, but as you'll quickly notice, the .45 ACP is an entirely different cartridge than the .45 Colt, and the .454 Casull looks like an extended .45 Colt. However, all three cartridges are the same caliber - .45. Furthermore, which one is a "regular" .45? Beats me. But I'll bet the .45 caliber cartridge most often refered to in this forum is the .45 ACP.
I hope I haven't muddied things up even more for you. One of the best souces of information like this I know of is Frank Barnes's book, "Cartridges Of The World." You can find it at most stores that sell a lot of ammunition and reloading supplies, or at amazon.com. Sometimes us old guys, who have been around different guns and ammunition most of our lives, tend to use words like caliber, bullet, and cartridge as if everyone should know what we're talking about. I suppose it's not much different than my wife (a computer whiz) trying to teach me about this computer. When she does, we usually end up in a shouting match. I just don't get it - why is it alright for her to say things like "click on that," when she means "DOUBLE click on that?"