The difference is the same as in powder, but on a smaller scale. But since the primer spark is the first step, the difference there snowballs. Joe mixes 3 parts of compound A and 2 of compound B, along with some other proprietary crap to make his primer... Sally does the same thing, but her compound A, B, or proprietary crap will probably be different for a number of reasons, including but not limited to secret family recipes, trade secrets, and so on. So Team Joe's primer will spark in X time frame, while Team Sally will spark in Y. Seems like a small thing, but given that we measure this stuff in GRAINS, and I still have 10 fingers and want to keep all 10, I'll play it super safe.
Primer isn't necessarily powder. Even way back when, it wasn't necessarily the SAME powder. Current primers, and I may be a little off on this, but it's how I imagine it anyway being layman who buys little metal bang buttons someone else made to go in bigger metal bang buttons.... but basically my limited understanding is that a primer is more volatile than powder. A primer is a metal cup filled with a glop of stuff designed to spark when struck. This glop dries inside the cup so it doesn't ooze out of the cup when it's bottoms up or otherwise oriented.
There's a metal plus sign type of apparatus that goes on top of the crud... your firing pin strikes the back of the primer cup which flexes the glop against that metal plus sign which can't go anywhere because of the primer pocket it's up against, not that that's important because those things will go off even if there's nothing on the other side of the anvil... it just helps. Anyway, because that glop gets shoved against the anvil so hard and quick, it ignites from the contact... which shoots a spart through the hole in the primer pocket which ignites your powder.
As for why it's called a 250 or a 215, or a large rifle magnum, or a small pistol primer, or what have you.. they have to call it something... I'm sure if these companies made cars, some of us woud drive "Car" and some would drive "Truck" and some would drive 280Z's.
Edit: Bad me, muscle memory had me type black powder instead of powder.