These groups are supporters of General Morden, the main boss from Metal Slug 1. It's set 2 years after Metal Slug 1, various factions from around the world are joining forces and is wreaking havoc. Story wise, nothing was changed from Metal Slug 2.
You can check this previous review of mine of Metal Slug Metal Slug X on Vita SNK did a marvelous job upgrading this game and filled in the holes that were obvious in Metal Slug 2. It still has the same cleverness, humor and action pack game from the original one but with some improvements that in my opinion made this game way way better than the original one.
Metal Slug X was released 1 year after the original game. This game is the upgraded version of Metal Slug 2.