As confirmed when Modern Warfare 2 was originally announced, Warzone 2.0 is "the new, free-to-play battle royale Warzone," so although it's built on the same technology that's powering MW2 you won't need to purchase that full-price release to get access to it.
The integration of Modern Warfare 3 into Call of Duty: Warzone will completely change the Battle Royale experience, including the new map. Call of Duty: Warzone is being revamped ahead of its first season release alongside Modern Warfare 3.