Augmented chords are a composite of the major chord formula, containing the root, third and raised fifth. (e.g. C+ formula is R, M3, and 5♯ (C-E-G♯).
Augmented seventh chords, (such as C+7) are a variation of a major seventh chords, in that they contain a raised the fifth along with a major seventh interval (i.e.. R, M3, 5, and 7). Therefore, a C+7 would contain the notes C-1st, E-2nd, G♯-sharp 5th and B–7th.