Creators, Producers, and Contributers are Lore Roles, similar to accrediation for film, tv, etc. Lore Roles are help build the mythology of the game.
Creators are the people who create a game. If you ideated the game - you're a creator. If you and a partner both collaborated on the idea - you're both creators.
Creators are frequently self-desginated.
Producers are the people who develop a game. A game isn't a game until it's part of the shared culture.
Producers are the people who take a created game and help shape it into a form that everyone loves and enjoys. They might not made the first version of the game, but they fundamentally alter the game and bring it to the masses.
Producers are frequently designated by Creators.
Contributors are the people who refine a game. Every game has edge cases, scenarios that have been missed, rules that need tweaking, or new rules proposed altogether.
Contributors update and correct a game, without fundamentally altering it. Contributions are on-going - think of how many Molokais have been discovered years after invention!
Contributors are frequently self-designated, as well as designated by Producers, Creators, and other Contributors.