I often see them used interchangeably, and I’m not sure if there is a real difference. They mean pretty much the same thing, though forever is used more commonly than for ever. I think in the states they say only “forever”. I could be wrong, but I think forever is more of a noun, synonymous with eternity. For ever is a phrase, meaning, basically, “for always”. “for”- a preposition “ever”- eternally, perpetually, constantly. I’m not sure if there is a grammatical difference, or just a difference in connotation.