Yup, a G2 chord is not a correct way to call out a chord regardless of how common it is...it's very guitar-centric terminology...and lazy, imho.
Gsus2 is a G major triad (G,B,D) but the 3rd note (B) is replaced with an A note and typically played an octave-and-one-step above the root to avoid dissonance with the root.
Gadd9 is a G major triad (again G,B,D)and includes an added 2 or 9 note (A), usually (but not always) played an octave-and-one-step above the root.