Some people regard the terms as being the same, while others regard the form 'newb' as being kinder than 'n00b'.
In any case, people who do really stupid stuff in games (like dropping grenades in the middle of their formation, teamkilling through idiocy, and basically acting like they have no idea what they're doing) are more likely to be called n00bs. Likewise stuff like posting on message boards with bad spelling, bad grammar, and no apparent attempt at basic etiquette. The term is also applied to people who try to make stupid and obviously incorrect statements while asserting that they have knowledge of the area - an assertion typically disproven by the content of their claim. "You know, Microsoft has never worked with IBM hardware, ever." or "Half-life was the first game ever to feature a 3d environment."
Newb is more often used to denote inexperience - for instance, someone who is trying to learn, or who maybe is just really bad at throwing grenades, but at least knows that they're supposed to be thrown at the enemy. In a forum, they may still be rough on the spelling, grammar, and even etiquette, but at least they're trying. It can also be used to denote newness to a particular community (and therefore inexperience in the local conditions), but this meaning is more common on the form 'newbie' than on the shortened 'newb'.
newb and noob/n00b do overlap in meaning and usage somewhat, and I've seen people argue that all-alphabetic forms (newb and noob) are a bit milder than the l33tsp34k forms (n3wb/n00b), but I'd take that with a grain of salt. Also, to really contradict what I just said, sometimes the word (any form) is simply used playfully, and isn't an insult at all (or at least, not a real one).)
I would have just searched wikipedia for its article and posted the address, but I'm bored right now. And, in other news, if you read through this post, you're a noob. (j/k;))
*edit* I may as well post the wikipedia address anyway, for those who want to see:
http://en.wikipedia.org/wiki/Newbie */edit*