It makes a lot of sense to split it up like that. My early experience (throughout college) was some full-time roles (that I quit e.g. to accept a FAANG internship, which I think I would be foolish not to), some project-based work, and I list all of that as regular work experience. It's clear to me now that this causes some confusion.

I really appreciate you taking the time to explain this to me as someone who is on the other side of the process, and I'll incorporate this knowledge in my resume (which, it looks like, I need to fully rework).