Personally I count rock and metal as slightly separate genres, latter being a bastard son who moved away and started its own life but his parents are still rock. This might make your job a bit easier.
I can only cover some basic genres of Metal-side of rock, with short explanations of each as I see them anyway. Someone else can explain Rock genres, as I know very little about them.
Early Metal. Not really a metal genre, but rock bands which gave Metal its basic sound. Black Sabbath is considered the father of all metal.
Heavy Metal. Or New Wave Of British Heavy Metal for long name.
Here metal moved slightly away from Rock song structure and became bit closer to classical in structure and melodies. And add some omnipotent and larger than life attidute. Iron Maiden is probaply most known band of the genre, as is Judas Priest.
Thrash Metal. People started mixing Metal with Hardcore and Punk. Straight forward, fast and angry and face pounding. Vocals also turned to shouting/barking, even screaming. Early Metallica, early Slayer, Kreator, Testament, Demolition Hammer.
Doom Metal. Continues where Black Sabbath left, with its slow, doomy and melancholic atmosphere. Sometimes vocals are clean, sometimes screamed/growled. Candlemass, Swallow The Sun.
Power Metal. This is confusing as there are two different Power Metal styles. One (and original) is basically something between Heavy Metal and Thrash Metal, more "powerfull" than Heavymetal that is. Other one, which is more known version, is style which relies on epic symphonies and fantasy oriented stories. Dungeons & Dragons of metal that is. I can only give examples of latter version. Manowar (technically just heavymetal, but father of this style of powermetal), Rhapsody, Dark Moor, Blind Guardian.
Death Metal. Slowly evolved from Thrash Metal. Often fast, definetly angry and violent, but not necessarily as straight forward, and usually handles very extreme and gory and/or occult subjects in lyrics. Though some thrash bands also had such but Death Metal is more known from it. Vocals are mostly deep growling, "cookiemonster style". early Death, Morbid Angel, Slugathor, Dismember, Cannibal Corpse, Malevolent Creation.
Black Metal. Despite being my fav genre, I'm not really sure what genre this evolved from, other than it got its name from Venom's song Black Metal. Subgenre mostly known of its very occult and Satanic themes, though they are mostly only metaphorical. And there are exceptions to those themes too. Where deathmetal is more "Thrashy" and pounding, Black Metal is more melody and atmosphere driven, often very minimalistic and relies on heavy repeating. Instead of angry and brutal its more cold and hateful. Vocals are usually high pitched and ghastly screams. Album production is also often very dirty and gritty which enhances the atmosphere. Immortal, Bathory, Darkthrone, Mayhem, Ondskapt, Drudkh.
Funeral Doom. Basically Doom Metal taken to extreme, to the point that some bands barely even resemble metal music, and is more closer to some kind of Ambient music. Slllooooowww, deeeeep, baaassssy, just creepy and even disturbing sometimes depending atmosphere the band aims for. Catacombs, Wormphlegm, Ahab, Skepticism, Mournful Congregation
There is also Progressive Metal but frankly I cant tell you anything about it as I dont really understand the whole Progressive genre. Dream Theatre is one known band though. Opeth can be fitted here too, with some deathmetal mixed in.
Then there are kazillion different sub-sub genres, but they are pretty much self explanatory as they just state what aspect of such genre is emphasized, or what bands theme is or what genres they have mixed together.
For example, Brutal deathmetal, Viking Metal, Folk Metal, Suicidial/depressive blackmetal, Blackened Doom Metal, Blackened Heavy Metal and list goes on and on and on and on and on... Its actually sometimes bit ridiculous, but this type of categorying is needed (in moderation anyway) to separate band styles from other as there are million different ways to play metal music.
