Amon Amarth is a bit of both(enigma) said:but then youre missing:
progressive metal
hardcore
metalcore
grindcore (and whatever other 'core' styles there are that i don't know about)
nu-metal
funk metal (and various other fusions)
not sure id agree on viking/death metal being grouped as the same thing though, death metal is usually a lot heavier. plus the whole cookie monster vocals. but then i havent heard a lot of death metal so i could be wrong there.