Are cap and ball, and black powder just different terms for the same kind of weapon or are there differences?

ball is the projectile; blackpowder is the propellent...

Black powder is the propellant as mentioned. It also refers to Pyrodex, American Pioneer Powder, Goex, Swiss, Triple Se7en and others out there on the market.

Usually when they talk about a cap & ball they are refering to a percussion cap type weapon. Meaning the musket cap or #11 cap, where you cap the nipple, and that spark from that cap is what fires the main charge. This can be used to describe percussion cap rifles or revolvers.

Of course there are flintlocks also. This is when the striking of the flint against the frizzen produces a spark which ignites powder in the pan of the rifle. That spark in the pan then passes through the vent liner into the main charge of the rifle which is then ignited.

Many times you here people refer to a cap and ball revolver which was a common six shot black powder revolver ignited by caps.

Ball of course is the projectile called a round ball. They vary in size according to the caliber. There are also conicals which are more of a slug type projectile, then bullets, and sabots.