Physical anti-realism is skepticism that our senses are true. In short, absolute denial that prediction or understanding of the physical world is possible.
Moral anti-realism denies that there is a universal value system for humans. It's related to, but possibly not identical to moral relativism.
Edit: As discussed below, my definition of Physical anti-realism is substantially misleading, even as a pithy summary.
Yikes. "X" anti-realism is the position that there are no objective (mind-independent) facts about X. So moral anti-realism, for instance, does not deny that there are universally shared values in humans, it simply denies that those values are anything more then attitudes. When an anti-realist hears "murder is wrong" she either thinks "That's not a proposition and therefore, neither true nor false." (non-cognitivism), "That's true because we both hold a very low opinion of murder" (subjectivism) or "That's false...
From Being a Realist (even if you believe in God):
My mother, who doesn't call herself a theist (I think she's agnostic), doesn't even accept realism. She doesn't even agree with this:
That's little more than tautologies here. Yet it elicited an impression of being forced to believe. I know because she told me about the totalitarian dangers from such narrow thinking.
I'm happy to have finally found the root cause of our ongoing disagreement, but now, how can I deal with that? It looks pretty hopeless, but just in case, does someone have a suggestion, or should I just leave it at that? (My ego doesn't like it, but giving up is an option.)
Now I'm relieved to know that in near mode, she's a complete realist. This craziness only shows up in far mode.