I don't know... it's all so confusing because there's so much info scattered across so many books, not to mention information that she's given solely in interviews or on her site or whatever. It's hard to keep track of it all. But yeah, I'm pretty sure James was a pureblood. I'm probably wrong, but oh well.
Is magic use genetically based or something for wizards to start making racial descriptors of it?
It isn't decided genetically, it just picks and chooses.
Pureblood wizards would have had two magical parents and magical ancestors (how far it has to go back, I don't know). Pureblood wizarding families are slowly becoming extinct.
Mudbloods are wizards/witches whose parents/ancestors (again, not sure how far it has to go back) did not have any magical abilities.
Half-bloods have one magical parent and one non-magical parent, apprently, although this issue is weird; both of Harry's parents were magical, but he's still considered a half-blood because his mother was a mudblood, I believe. Voldemort's father was non-magical IIRC.
Squibs are those who are born into wizarding families who either have no magical powers themselves or very little magical powers.