Yes, that's the whole crux of the matter, naming conventions evolving. It makes it difficult at times, that's why to write Cm7b5 is a better way to describe the half diminished 7th. No doubt then.

From the traditional theory angle here, if I had a student who in a theory exam paper wrote the notes C,Eb,Gb,Bb for a Cdim7th chord, I would mark them wrong. I would tell them that they had written the notes for the C half diminished 7th chord.

Good discussion!

yjoh

[i]Music...a joy for life.