“Old” call of duty is based from WWII, which were made in the early 2000s inspired by Medal of Honor while “New” call of duty is the fictionalized takes within the FPS genre (basically the ones you recognize today). Modern Warfare (the 2007 one) is the title that departed from the WWII genre while World at War tackled at both theaters of WWII (the Pacific and European).
Cod Blops 2 was peak CoD IMO. MW and MW2 was where they really figured out the formula. BlOps 1 was where they figured out it needed to still be fun and innovative. MW3 kinda sucked, and BlOps 2 was where they got everything right for the last time. Ghosts was still recovering from all the mistakes of 3, and BlOps 3 completely lost the plot. CoD occasionally remembers that simple gunplay was what made it famous, but nowadays, all online games are about whale fishing, so we’ll never get better than BlOps 2.