I hope I have this right (I'm no expert).

The "degree" symbol stands for fully diminished seventh, which is a stack of minor thirds. It is like taking a (dominant) seventh chord and flatting the third, fifth, and seventh.

Cº (C with degree symbol) is C Eb Gb Bbb same as C Eb Gb A

If you stack on another minor third you get back to the C. Not counting inversions there are only three of these chords, since for example,.Cº = Ebº = Gbº = Aº.

On the other hand
Cdim7 is C Eb Gb Bb
I believe these are sometimes called half-diminished seventh chords.