A lot of 'nu-metal' bands are considered alternative metal bands. Are the two genres different? I believe there is a slight difference. So the main question is... are they the same? What makes them different?
In the most basic way: Black metal: Highly distorted, fast played guitars, heavy use of double bass and blastbeats, gurgling, screaming vocals (think crows). Lyrics deal with Norse mythology, satanism (especially in Scandinavia), but also depression. To get a taste of it, try Immortal, Darkthrone, 1349.
From Wikipedia: Nu metal is a musical genre that typically fuses influences from grunge[1] and alternative metal of the 1990s with funk music, hip-hop, and various heavy metal genres, such as thrash metal and groove metal. Some nu metal bands: Linkin Park, Korn, Limp Bizkit,Papa Roach Black metal has lots of distortion, high pitched shrieking vocals, and a fast pace similar to thrash though it also frequently involves itself with anti-Judeo Christian themes. Some black metal bands: Venom, Bathory, Mayhem, and Darkthrone. Death metal shares most of the elements of black metal except it usually has low growled vocals sometimes nicknamed Cookie Monster vocals after the Sesame Street character and obviously a lyrical preoccupation with death and violent imagery. Some death metal bands are Entombed, Carcass, and In Flames. Thrash metal is a subgenre of heavy metal music, one of the extreme metal subgenres that is characterised by its signature high speed and aggression.[1] The origins of thrash metal are generally traced to the late 1970s and early 1980s, when a number of bands began incorporating the sound of the New Wave of British Heavy Metal (NWOBHM),[2] creating a new genre and developing into a separate movement from punk rock. This genre is much more aggressive compared to its relative, speed metal. There is often significant crossover from one metal category to another, and the influence of non-metal genres, including classical music and jazz, is not uncommon. Bands playing thrash metal include Testament, Nuclear Assault, Megadeth and Slayer. For the other metal genres, see link below...