Good question, Lea. I don't think there is any difference at all. The New Oxford Dictionary for Writers and Editors (which dictates OUP practice) gives "for ever" as an alternative to "forever". But in US English, I think "for ever" is rare. I almost always write this as one word, forever. The only time I can think of when I would write it as two words would be "for ever and ever", where the second ever is just for emphasis.