The lines can be a bit vague at time. Death Metal was derived from Thrash - it basically took Thrash, and stripped it down even further to its most basic elements. Early Death Metal bands (Possessed, Incubus - the band now known as Opprobrium, pre-Arise era Sepultura, Graf Spee, etc.) were still Thrash bands at their core. In the 1990s, Death Metal sought to further the gap between Thrash bands and themselves, and turned to Hardcore Punk and its derivatives (Powerviolence, Crust Punk, Grindcore, etc.) for influence - this is especially apparent with bands such as Cannibal Corpse, later Morbid Angel albums, Deicide, etc. Thus, your more modern Death Metal bands tend to be quite distinguishable from Thrash bands, whereas earlier Death Metal bands drew a much finer line.
