That's what Nu-Metal is?
Jeez, back in my day, we just called it rap-core.
Down here in South Fla, it was even referred to as Crossover - but crossover was just a name for bands that mixed styles of music (rap and metal?). Nonpoint was one of the biggest crossover bands (they're with a major now and apparently got dicked over) - they used elements of hip-hop, hardcore, latin/tribal music... kind of like Puya with more hip-hop. Then there's Groovenics who mix ska/hardcore/booty-music(

)/groove(?) - Anyway, yeah, we just called it crossover, not "Nu-Metal". You kids with your new genres... .
Anyway, as far as "Nu-Punk"... . LOL! Well, we just called that Pop-Punk. Personally though, I see that as pop... with the band sometimes doing punk inspired songs. To be honest, though, I would even be so bold as to call bands like Linkin Park and POD pop too.
Though, not that I never liked POD - I remember back when they were a Christian band. I really liked that song where they had that Spanish-guitar - I remember the video but not the name. They looked like a Mexican ass KoRn hanging out in some abandoned mill or something.
Edit Note: I remember Deftones being called "Ambiance". Personally, I think that's suitable. I can't believe I've never heard of Nu-Metal before. Is there "Nu-Hardcore" too... or does hardcore not exist anymore?