Raedwulf: Well, now I have looked it up. It does indeed turn out that both words go back far into Old English and the Danes are not responsible for either. The other part of what I said -- that they were originally synonymous but people have come up with a variety of distinctions over the centuries, is amusingly true:
1. Beer had hops; ale didn't.
2. Men call it ale; gods call it beer.
3. Ale means the paler kinds, for which the malt is not roasted.
4. Various localities have made their own distinction. (I suppose that takes care of California.)