Yeah you could probably define genres/subgenres by taking a look at the defining bands.
"Metal" in general: makes me think of NWOBHM bands like Iron Maiden and Judas Priest, for some reason.
Death Metal: Morbid Angel, Death (first two albums anyway), Obituary, all those buggers
Black Metal: Early Bathory, Emperor, Darkthrone, etc
Power Metal: Blind Guardian and... fuck, I'm not really too familiar with this genre. Dragonforce, Nevermore, and Symphony X are power-y, I suppose.
Prog Metal: Dream Theater, Fates Warning, Queensryche
Same is true for the more specific subdivisions (Suffocation, Nile, Cryptopsy are all example of tech-death, Opeth is prog-death, Meshuggah is prog/"math" metal, and so forth).