When I (frequently) come across this type of chord, let's say starting on C:

C Eb Gb A (or Bbb)

is it called a diminished 6th, as C to A is a sixth, or is it a diminished 7th, as Bbb to C is a diminished 7th?
Or are they the same thing?

Sorry if it's blindingly obvious but my somewhat diminished brain cells can't quite cope ..!

It depends on how you spell it (whether it's A or Bbb).

When written as a C Eb Gb Bbb, it is a diminished 7th chord. C to A is a major 6th, not a diminished 6th.

A diminished 7th chord is contructed by piling minor thirds one on top of another, which is why it has to be Bbb and not A, and therefore the two outer notes form a diminished 7th interval, which is why the chord is called a diminished 7th chord.

I think you mean C to Bbb is a diminished 7th ! Not Bbb to C. !
That is certainly the notes of a Diminished 7th.

However it depend what you call the notes, for example B to F is Diminished 5th, but B to E# is an Augmented 4th
But to play them is the same.

A diminished 7th consists of nine semitones. There are nine semitones between C and Bbb.

C-Eb-Gb-Bbb is a diminished seventh chord in root position. Since C is the chordal root, the chord is expected to resolve to a Db major or Db minor chord.

C-Eb-Gb-A is a diminished seventh chord in first inversion. Since A is the chordal root, the chord is expected to resolve to a Bb major or Bb minor chord.

By the use of enharmonic spelling, the same diminished seventh chord can resolve to different harmonies. This allows composers to explore modulation into distant key areas.

Thanks all.
I think glimmers of light are creeping in. I remember now about the minor thirds piling up and of course Gb to A isn’t, though it is in terms of sound…. it’s not wise reading this after two large glasses of wine!
I think I was thinking; root + minor third + diminished fifth is a diminished triad, and C to A is a sixth, thus diminished 6th. There might have been some logic in it somewhere! So much for do it yourself theory!!
It’s a bit like words that sound the same but spelt differently, innit?