pig: "probably from Old English *picg, found in compounds, ultimate origin unknown"

Pork, because we usually use the adjective porcine for things relating to pigs. As mousbear mentioned, from Latin.

The different names often have to do with different cultures or different cultural statuses within a culture. I think I read once that certain animal names and cuts of meat have come partially from "vulgar latin" and others from "proper latin" so you sometimes end up with two names for the same thing. I'm not sure how accurate it is though.