Both.
Look how Death Knights in WC2 were Orc Necrolyte spellcasters in the corpses of fallen Knight bodies, while the Death Knights in WC3 were all corrupted Paladins (still living) who followed Arthas into Northrend, and now WoW Death Knights are any race/class that died and gets raised into the Lich King's service. All 3 different origins and concepts, with the general use of unholy magic being the common thread between them.