I think, perhaps, that I see the two versions as similar in relationship to 'all ways' and 'always' - not meaning exactly the same as each other - as Ningloreth and the Cambridge Guide to English Usage seem to suggest as well.

'All right' suggests that all is right - 'alright' suggests that things are just about acceptable.

Also of course, you wouldn't say "All right," as an agreement to do something, I don't think - as in

"When you are out can you get a bottle of milk?" "Alright."

Or would you actually have to write

"When you are out can you get a bottle of milk?" "All right."?

Which just looks silly. Well, to me, anyway.