Def2-SVP has the polarisation functions on all atoms, -SV(P) does not have these functions on the hydrogen atoms and -SV does without them.
In future, you can check on the EMSL Basis Set Exchange - https://bse.pnl.gov/bse/portal - It wouldn't give you an answer explicitily, but you can view the basis set for different atoms and see how the different sets vary.
A side note - If your 'complex molecules' aren't too large, consider the larger Def2-TZVP basis set. Errors at the Def2-SVP level can be several kcal which may significantly impact your study. As an alternative, consider the PC-n family of basis sets from Frank Jensen. If the Def2-TZVP set is too large, the double-zeta PC-1 might work well.