OK, being a little high right now, I had a moment of wondering if maybe I've just been using a totally made up word my whole life. So I googled, and MW says that while it is a word, it's less common than all right, which I find very weird. I swear I see alright used way more often, but I suppose the written things I'm exposed to are somewhat limited.
But it got me thinking, I wouldn't have said that the two have exactly the same definition. To me all right sounds much more affirmative than alright. Or at least there are more varied uses for alright: as a happy exclamation, as a way of saying good but not great, or as a way of saying things are perfectly normal. All right only really fits the last definition, at least to me.