Modern Warfare 2 is a soft reboot rather than a remake of the original. Modern Warfare 2 (2024) is not a remake but a soft reboot of the original story, which has been enhanced for modern storytelling. It follows a similar storyline, with many connections and links to the previous trilogy.
By most definitions and easily made observations, Call of Duty: Modern Warfare II is not Call of Duty: Modern Warfare 2, a 2009 installment of the game with a very similar name but, as you can see, a 2 instead of a II. Their stories are different. Their mechanics are different.