Phantom Forces itself doesn't got a official backstory. However, there are many things in the game which can tell a story or two. All the information here are just a speculation; nothing is confirmed.
The conflict represented in the game might have been caused by the StyLis Studio company (an in-game version of the real StyLis Studio).The company seems to produce many products, two of them being the Phantom Energy and the Ghost Cola. The company could have been controlled by two teams, the Phantoms and the Ghosts, both competiting for domination.
The Phantom team main color is orange. Hints lead that the team might be an american force.
The Ghost team main color is blue. The Ghost team might be a russian force.