I’m not sure that sus2 is a normally accepted jazz chord terminology. Also add2 is really unnecessary as the correct term for this in my view is add9. As previously stated the add9 is a chord with a ninth but without the normally included 7th. However when you have 9ths or add9ths the exact voicing of where the 9th is placed is not set in stone. For instance in the case of C9 you could voice it as say (from bottom to top) c,e, g, bflat, d or equally you could voice it c, g, bflat, d, e. In this latter voicing the 9th is placed just under the third. The piano player or guitarist is given free license to use their own taste in how it is voiced. The same applied to an add9 chord. Sus2 is a slightly odd and unclear terminology I think. If you want a chord of C with no third and which includes a d then you might for instance write Gsus4 instead or Gsus4/C! The jazz chord system quite often breaks down and becomes unclear at times and writing full notation might be preferred.

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