I think you need to review some fundamentals about the triad types and their practical origin.
First you must understand the foundation is the diatonic gamut. You can describe that several ways but a common one is to say it's the white keys of the piano, or
C major, the group of pitches
From that selection of tones you stack up thirds on each tone to create triads, like this...
...notice it is the triad on
B on the
VII seventh scale degree, the leading tone, which is the diminished triad. It is the only triad of the group that is diminished. The leading tone triad is the fundamental diminished triad. In terms of stacked thirds it is two minor thirds, but in terms of the diatonic gamut it is the particular quality of the triad on the leading tone.
Minor key music is more complicated, because accidentals are used in combination with a key signature, but the basic diatonic harmonies in minor will be...
...notice now the triad on
B is on the
II second scale degree, and also the
VII seventh scale degree takes a sharp. Both the
VII chords are diminished in minor keys.
Notice also that the augmented triad doesn't appear in these particular diatonic chords. We can skip over the details of that and simply say there are four triad types:
The two patterns of diatonic chords above can be transposed into any key.
Lower case roman numerals and the
o circle sign are often used to label diminished chords, like
iio, but sometimes you will see only upper case Roman numerals used and the chord qualities are understood from the major/minor context.
Diminished chords are not a kind of minor chord. Yes, both the minor and diminished chords have a minor third, but they a considered different types of chords.
The various qualities of triads come from the diatonic chords and their position in the diatonic scale, the intervals between the tones in those positions, determines the triad qualities.