Death Metal is a form of music evolved from thrash metal in the 1980s. The band Death popularized the name with the song "Death by Metal" (as well as their own name). The song by Possessed also gave the entire genre a debated name credibility which is still disputed to this day.
Death Metal is catergorized by its gutteral growling vocals, thickened guitar tones with sometimes heavy distortion properties, and blast beats which can range from a normal to very fast speed. The vocals and drumming are the pure tell-all of a death metal band, the gutteral bellows are began in the stomach yet shaped with the throat to raise and lower the pitch of the music in general, while the drumming is blast beat and dependant (mainly) upon the bass drums. Independant variables to be added to the mix are amounts of groove, morbidity, technicallity, and speed.
Death Metal itself has evolved slowly through the years, ranging from the olden days (Deicide, Death, and Morbid Angel) to the now modernized sounds of Death Metal, (Vital Remains, Cryptopsy, and Hate Eternal) and even now to the more "Brutal" scene of Death Metal (Deeds of Flesh, Severed Savior and Beheaded). Death Metal also has grown roots into the Grindcore scene and evolved many Death/Grind bands, evolved into Gore Metal, and numerous other forms of music.
Slayer is not a Death Metal band. They are a thrash metal band. Cannibal Corpse are not a Gore Metal band. They are a Death Metal band.