Well, a sus2 definitely has no 3rd, but an add9 can have no 3rd too. Generally I'd call it a sus chord if I wanted the tension pulling it to resolve to a 3rd, and an add9 if not. I think the distinction is similar to modes...same note but it's useful to call out what function you want those notes to play.
I started responding before the OP was edited to the "not revealing" thing. Not sure what that means.
A9 is a dominant chord, and contains A C# E G B (assuming no notes are dropped to aid voicing). Aadd9 is an A major triad with the 9th added (hence the name): A C# E B. Asus2 has no C# in it: A B E. Asus4 also has no C# in it: A D E. If the C# was included, this would be written as an Aadd11. If it had the C# and the dominant 7th, G, it would be A11, and when voiced fully would contain the notes A C# E G B D. That chord is quite a 'crunchy' one though, and is used less than A9 or A13.