How Many Elementary Particles Are There, Really?

Even though "particle photon" and "wave photon" are used alternatively, they are just convenient ways of talking about the behavior of the same "photon field". The same way when we say "it is raining" we don't mean that there is a "it" that "rains", we should try avoid taking these descriptions too literally.

That being said, is difficult because we are using language to describe very-much-not-everyday stuff. We all need mental hooks to anchor new knowledge and most of our intuition is based on the classical (not-quantum) world aroud us.

You don't have to wonder, because they are. They're manifestations of fields.

I think it is a reasonable answer to tell people "if you're looking for the short list of simplest things, the number of types of fields there are is probably what you're looking for".

That doesn't invalidate this question in general, though the number of different answers from people looking at the same thing suggests it may be underspecified.

That's what the various string theory proponents start from. There's "too many" different subatomic particles, so there surely must be something smaller that they're composed of?