What mark said, although I am not familiar with the regular third, flat 5 diminished.
To me the BIG deal in this question is “What is the difference between a major and a minor chord?” These chords sound emotionally opposite. A major chord is happy. A minor chord is sad. What separates them? Simply moving the second note of the chord down a half step. So to put that in real notes: Let’s look at a C chord:
C (major) chord is Root: C Third: E and 5th: G. Just three notes, but you could of course add octaves of those same notes up or down.
Cm (minor) chord is Root: C Minor Third Eb (E flat) and Fifth: G. Again, just three notes. 2 of the notes are the same, but simply moving the “middle” note down a half step totally changes the character of the chord from happy to sad.
The major and minor chords are the basis for much music. If you understand that difference, you are at a strong position. That major or minor third is very powerful. Interestingly, you can also remove the third for another type of sound. It can be happy or sad depending on the context. To me it sounds more powerful. In the example above that would be a C5 chord. Play as many notes in the chord as you want, but they all have to be C and G notes.
Extra info… skip this paragraph unless interested. To me the diminished is just a “scary” mod to a minor chord, and the augmented chord is just an oddball. However, both are mathematically interesting. In a diminished chord the notes are 3 semitones apart. Add the dimininshed 7 up 3 more semitones, and the pattern repeats. The chord can legitimately be considered 4 different chords. Similarly, in an augmented chord the notes are 4 semitones apart. So, this chord could be three different chords depending on context.
Note: oaklymaple posted as I finished this.
I hope that helps!