Each game is set in a completely different time period. Modern Warfare 2 is set in the present day, while Vanguard is set in the midst of World War 2 - this means all the weapons, vehicles, and maps are completely different.
As with Cold War, Vanguard is integrated with Warzone, allowing players to progress and use weapons, operators and other cosmetics items across both titles, in addition to the existing Modern Warfare and Cold War items in Warzone.