I'm not very familiar with nu metal, just Toxicity and the stuff my coworker used to play. But the first thing that strikes me about nu metal in comparison to "metal metal," is that nu metal seems poppier. I mean, having catchy choruses is nothing alien to metal. I don't think Pantera did more than one song that didn't have a big, beefy ass chorus. However, chorusy metal bands still tend to have an instrumental focus, long instrumental passages, things like that. Nu metal seems to be just verse/chorus/verse, as much like grunge as metal.
As far as defining nu metal, I'm certainly not qualified to do that. But I'd say it's the wave of metal-styled music that followed the end of grunge and the rise of suburban hiphop. It seems to mainly be chugga-chugga music with accessible song structures and influence from rap & industrial.