While those latter two aren’t connected to the new MonsterVerse, neither are all versions of Godzilla.
As the King of the Kaiju, the giant lizard has served as the unofficial mascot for monster movies in general.
Over the years, there have been many iterations of Godzilla created.
With the success of both films, Legendary are poised to dominate the market on kaiju films, especially considering The Great Wall and Pacific Rim are also their creations.