Even if we use "wave photon" and "particle photon" alternatively, they are only convenient ways of talking about the behavior of the "photon field". The same way when we say "it is raining" we don't mean there is an "it" that "rains" we should try to avoid giving too much litteral meaning to these descriptions.

That said, I get it is difficult, especially because we are using everyday language to talk about very-much-not-everyday stuff. We all needental hooks to anchor new knowledge and most of our intuition comes from the classical (not-quantum) world around us.

As a physicist, I feel the art is in learning when to use what description, what Sean Carrol calls "poetic naturalism".