“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).
This weekend, the Modern Warfare 4 Beta is public if you want to try that. Also Black Ops 7 Endgame is free until Season 5 ends. I enjoy the latter one very much, despite my last CoD game was probably… the first 2 or 3 releases they had. They are very different games now, but the Endgame in BO7, I like to solo most of the time to wind down.