Minor relates to the 3rd of the chord
Diminished is generally related to the 5th of a chord
The minor ii has a flat 2nd, but a “perfect” 5th
The diminished vii has a flat 2nd, minor 3rd, the flat (or diminished) 5th, and a minor 7th, but it’s mainly about being minor with that diminished 5th.
An augmented 4th would be the same note as a diminished 5th, but is usually referenced in a major chord. In the case of the major scale, the Lydian mode features an aug 4th which occurs naturally if you added a 4th to the Major IV chord.
The modes of the melodic minor and harmonic minor scales twist this stuff up a bit, which can be really cool. Lots of jazz folks like using the melodic minor modes to spice up their harmonic and melodic themes.
Never sure how clear this is when sharing with others. So, good luck. We’re all counting on you.