Hey Oolongtea,
Uncle Rod is right. Dimished chords are super unique compared to all the other chords you have learned because there are only 3 chord shapes which will make all diminished chords. To understand why I think it would be helpful to examine a diminished chord formula.
When I finished the UU+ lesson for diminished chords, Aldrine noted that the diminished chord formula was 1-b3-b5-6 (aka to make a diminished chord we need the first note, a flat 3rd note, a flat 5th note, and the 6th note of a major scale). For example, let us use the C major scale to construct a C diminished chord. The notes in C major are C-D-E-F-G-A-B-C correct? The 1st note is C, the flat 3rd note is Eb, the flat 5th note is Gb, and the 6th note is A. Thus these 4 notes (C,Eb,Gb,A) make up a C diminished chord. If you go to your fretboard you will see that chord shape you are talking about [2323] contains all these notes! Thus this is a C diminished!
But the name C diminished is relative to our C major scale. The C note is on the third fret of the 1st string which acts as a root. What if we wanted the other 3 notes, Eb, Gb, and A, to act as root notes also? Well then we would make an Eb, Gb, and A major scale and apply our 1-b3-b5-6 formula. When doing so we will find that no matter which scale we use, we will end up with our 4 original notes of C,Eb,Gb,A. Thus these 4 chords C dim, Eb dim, Gb dim, and A dim are all the same. If you write out the major scale for each scale and apply our diminsihed formula you will see that there are only 3 locations (that uncle rod mentioned) which make distinct diminished chords. Thats why multiple dimished chords correspond to the same particular chord shape.
I am sorry if this was too much music theory. I hope this helped! If I made any mistakes with that explanation, hopefully someone will correct me