Justin has a great lesson called “chords in a key”. He explains it a lot better then I, so I won’t even bother to try (Will add the link later).
Long story short, the “chords on the key (=diatonic) of C” are
C Dm Em F G Am Bdim
( if you want to know why, see the video)
As the chord “Em” is in the key or c it is a “diatonic chord” for the key of C.
Example1: E MAJOR is not in the key of c and therefore not a diatonic chord (in the key of c). Reason: should me major, but it is minor.
Example2: Eb Minor is not in the key of c and therefore not a diatonic chord. Reason: is minor but it should not have a b.
Triads have nothing to do with the stuff described until now. A triads describes a chord which is made up of 3 notes (3 = three = triad). As a contrast: Chords made up of 4 notes are (how Justin Calls it) “quadads” (or four note chords).
So a “diatonic triad” is a chord which is made up of three notes which belongs to a specific key. It would not make sense to say only “the G triad is diatonic” without referencing the key it belongs to. For example Gmajor would be a diatonic triad for the key of C and also for the key of D. It would not be a diatonic triad for the key of A (for example).