Yes you are correct that sound card is 5.1 not 7.1. 5.1 means it outputs up to 5 discrete channels plus a subwoofer channel (.1). To be quite honest, 7.1 is pretty overrated and somewhat unnecessary by my opinion. Others like it and find its better, you will have to decide.
As far as headsets, you may be able to use the 7.1 headset in 5.1 mode (not plugging in one of the cables). I think on headphones you will never notice 5.1 vs 7.1, again just my opinion.