I think there is a deep conceptual unlock: concurrency is about semantics, whilst parallelism is an operational property. I use this distinction a lot in my own work. Concurrent programming primitives are inherently non-deterministic (and usually about handling non-deterministic events), on top of which we must then establish some kind of properties (sometimes determinism to some extent). Many interesting parallel operations are however completely deterministic, and the fact that they are parallel is a property of their assigned cost model (and hopefully implementation, in practice).

I agree that this distinction is hardly universal, but it seems to be growing increasingly established, and I think it is worth fighting for it.

Personally I think it's not a good idea to think too rigidly about and try to draw a huge distinction between the two. They're on a continuum and sometimes I'd say some things aren't even strictly speaking "between" them either. Sitting down and trying to classify code into "parallel" and "concurrent" is as likely to do harm as to do any good.