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Sounds like you have things pretty well covered with your definitions. There are variations of design that may look like one, and actually be the other, and you seem to understand that, as well.

One thing to avoid, and something many don't do these days, is to talk about a certain design of mechanism that falls under a broad heading (like "striker fired") and assume that every design of mechanism that falls under that heading is the same. They aren't.

What I mean is the tendency for people to talk about "striker fired" pistols, such as the GLock and those that essentially copy that system as if they are the ONLY striker fired pistols. Some think a "striker fired" pistol is a modern polymer frame semi auto, only. When I hear that, I like to point out that a LUGER P.08 is a striker fired pistol, and so is a Remington XP-100 (bolt action).

The Ruger Mark series semi auto .22s LOOK like striker fired guns, but aren't, they have internal hammers.

I had an old pocket pistol some years back (Savage) that had a hammer, BUT was actually a striker fired pistol. The "hammer" was actually just a visible cocking indicator, and didn't fire the gun.

The original Thompson submachine gun is technically a hammer fired gun, though its hammer differs considerably from the usual system.

So, being aware that specific designs can vary widely, I think your terms are workable.