Isn't the address is same as wallet?
I'm not going to go into the technicality per se of what you ask, as some have given their full answers to a very simple question.
Arguing a question is basic, and in your case perhaps, my assumption, you throw yourself an answer in the OP, but by adding the "?" The transformation in doubt.
Someone could also observe that detail, before. So the point here is, the argument. Anyway, I answer you in simple words, it is not the address! the same as the wallet!
The wallet manages what the "public" address receives, hosts and wants to send.