Which is which?


The basic answer: Ale is a subset of beer. So is lager. Both ale and lager are beer.
Beers fall into two broad categories: Those that are produced by top-fermenting yeasts (ales) and those that are made with bottom-fermenting yeasts (lagers). apparently there are even hybrids too.

Ales came first, when brewers weren't exactly sure what role yeast played. Because ales were unstable, brewing ceased in warm weather and brewers would store reserves in as cool or cold an environment as they could find. Brewers storing their beer in very cold Alpine caves found that their beer was more stable because the yeast had sunk to the bottom.

and there you go.