metallica with bob rock = shitty 'country' style metal. The last thrash album they made was ...And Justice For All, which was pretty ordinary cause of the COMPLETE lack of bass on it.
guns and roses are hard rock.
I've seen Black Sabbath called heavy metal, and/or sludge, as well as some doom metal like Iron monkey being called stoner type stuff.
televators good job there, id just like to add - with Doom metal, there is VERY distorted, downtuned guitars usually, even moreso than Nu metal.
Nu - metal is played in Drop C tuning and does not feature solos (for the most part)
Cradle Of Filth call themselves Horror Themed Metal these days - becuase of their ousting from 'true' black metal. Usually they are described as playing Heavy metal with gothic/black undertones. Nymphetamine did not sound particularly gothic at all to me in any case.
Death are known as Technical Death Metal. a better idea of influential DM bands would be including Bloodbath, Cannibal Corpse, Morbid Angel, Deicide, Dying Fetus, et al... a spinoff of which you haver Brutal Death bands like Nile and Cryptopsy. To me brutal death has more lower end - more double kicking and blastbeats, as well as a sometimes more prominent bass line.
Grindcore is a sort of mishmash of Thrash metal and punk - songs are VERY short, often with screamed, indecipherable lyrics, and no bass to speak of. e.g Napalm Death, Anal Cunt
If you want to go even further, you can dig up genres such as Viking metal etc, but it gets a bit ridiculous.
an excellent metal site is
www.metal-archives.com