Thanks for reiterating what constitutes a diminished chord (i.e., all minor third intervals). I believe you have posted that explanation before - I'm glad you retyped it for lazy folks like me who didn't print it out the first time and were reluctant to do a search to find it again.
A chord naming program (nod to Tony Burns) I use called Nutchords makes a distinction between a *just plain* diminished chord and a diminished chord annotated with the little degree circle. From what I could see (or hear), it looked like the only difference was the *just plain* diminished chord had only three notes while the *degree circle* diminished chord had four.
From the above posts, I am to assume that the chord naming program seeks to differentiate between a *just plain* diminished chord and a diminished 7th chord (e.g., A#dim is A#-E-C#; A#degree circle is A#-E-G-C#), although what I am reading in this thread tells me there is a difference of opinion between jazz players and classical players as to how it should be notated. For purposes of distinguishing one from the other when using Nutchords, I'll assume that *just plain* diminished will be notated *dim* and consist of three notes, and diminished 7th chords will be notated with the little degree circle, and consist of four notes.