You know, a lot of people think that all metal is death metal. Let me explain.
As you know the biggest sub genre of heavy metal is in fact death metal. Almost ALL metal can fall under this category. So what I am going to try to do with my limited formatting skills is make a chart of all the different types of metal and examples of such bands. Observe.
It all started with NWOBHM other wise known as the New Wave Of British Heavy Metal. this is dominated by bands like, Iron Maiden, Motorhead, Def Leppard, Diamond Head, Tygers of Pan Tang, Girl School, and others. It was like many classic Rock bands but with a heavier more melodic sound. It spawned/influenced several future genres.
Next it was Thrash metal, dominated by namely the bay area four of thrash. (Metallica, Anthrax, Megadeth, and Slayer) also bands like Overkill, Razor, Kreator, and others. They took an even heavier sound slightly less melody then the NWOBHM and spawned all of extreme metal.
Next was death metal. Morbid Angel, Sepultura, Deicide, Cannibal Corpse, Nile, Death, and others. Even more extreme and notorious. And my personal fav sub genre of metal.
Then there is black metal, which takes its roots in thrash and death metal but with a completely different twist. Satan is the main subject matter of their lyrics. Bands like Emperor, Immortal, Carpathian Forest, Burzum, Darkthrone, Mayhem, Hate, Gorgoroth, Bathory and many others. This is by far the most evil metal there is. Satan's muse as it is called by Darkthrone.
Grindcore is another step in the direction of extreme metal. It is more extreme then death metal, whilst sounding almost exactly the same. Grindcore was invented by Napalm Death, with the groundbreaking album Scum, and was continued by bands like Nasum, Leng T'che, Anal Cunt, and others. It is noisy and hardy recognizable as music. It takes influences from, death metal and hardcore punk. Especially Dead Kennedys.
Goth metal, bands like Nightwish, and Evanescence, and several others. It is symphonic in nature and fantasy-oriented.
Next there is Progressive metal, the most mature form of metal. Opeth, Coheed and Cambria,
Katatonia, Porcupine Tree, all make up this fine genre. It is intellectual in nature and the more refined of the sub-genres.
I could keep going but that would be boring. More to come I guarantee you

Demonaz