@ArcticChar I'm not sure. I don't oppose it, at least. It would seem that a large proportion of FDEs are indeed delay DEs but not all of them. Wikipedia seems to very heavily use delay type ODEs as examples, only mentioning the existence of PDEs that depend on future times (which appear to be called "advanced differential difference equations" c.f. the tag I removed above)

The Wikipedia article also mentions integro-differential equations. Checking a few sources (as I am not an expert) like a paper of Falbo, and glancing through some books, I think its at least acceptable to say that those equations are functional differential equations