A rank gained in one will automatically carry into the other.
Starting in December, Activision is unifying progression across Warzone and Cold War with shared ranks, weapons, battle passes, and cosmetics. There is no longer a single de facto CoD. Warzone's longevity makes Cold War a harder sell. In fact, a better Call of Duty game released this year-the free-to-play battle royale Call of Duty: Warzone.
Despite welcome adjustments to Create-a-Class and a fun (if brief) campaign, Call of Duty has been a lot better before.