Just saying that perhaps getting really rigid about a specific definition of a term is probably not the most helpful thing. More important I think is that we communicate and work to understand each other’s meaning, and soak up some of the really good bits that are freely and generously offered here.
Relative to early and late (and I’m just a rec player), with no other context given then I've generally understood the terms be in reference to the contact point. I have also heard the term hitting early to be used in reference to hitting on the rise, but generally there’s context within which to understand that. I have not really heard hitting late to reference hitting a ball after it’s crested and falling. However someone wants to use the terms, the concepts are the important thing for improving our games.
So I’m going to put energy in defending my contact point, because I’ve personally found that mental image very helpful for improving my game.