In my opinion: non-vax is an umbrella term for anyone who has chosen not to vaccinate their children.
Non-vax is a spectrum, and it can mean anything from "not vaccinating at this time, but a I can see being selective/delayed at some point to no vaccines should exist.
Anti-vax, is the extreme end of the spectrum that believes no vaccines should exist. I would also argue that thinking all vaccines are stupid in all circumstances (but people should still be free to choose them) might be anti-vax.
Anti-vax is a pretty loaded term, and it is often used in a very derogatory fashion.
Sadly, some tend to regard anyone who questions vaccines or the vaccine schedule at all as a heretic and "anti-vax" (did you know Dr. Sears, who advocates most if not all vaccines, is anti-vax? SNORT)
(ETA: posted at the same time as Taxi, who said virtually the same thing