I know, we usually do this on the 3rd Friday of the month. Well, we didn't get to it then, so we wanted to get in before the month was over. While an archaic distinction, the question actually gets to the heart of artificial distinctions in the beer categorization system. In the United States we take great care to classify everything that gets brewed within the confines of our classification system that is generally spelled out in the BJCP Guidelines. When we (Americans) drink a beer we first want to know its style - what kind of beer is this? Then we want to recall what the style is supposed be - what are the general characteristics that I typically find in this style of beer? Then we want to compare the current beer to the style - how well does this beer match the style? And, frequently, we rate (BA.RB.) a beer based on that comparison.
Believe it or not, this does not occur everywhere. For examples, the Belgians do not, generally, make these distinctions instead classifying between blonde or brun and blended or unblended; they also have the abbey distinctions (abbey, dubbel, tripel). Very general classifications. On the other hand, the British (and Americans) have a lot of very narrow classifications, many of which are not even internally consistent (e.g., "porters" include both ales and lagers).
Having said all that, we get to the question: What is the difference between an ale, a pilsner, and beer?
To some extent we talked about this a few posts ago when we talked about Richard Owen and his Lake Brewery. We mentioned that the type of distinctions made there (ale, porter, and beer) are largely historical. In other words, "beer" is what we now call "lager" and "porter" generally is classified as a type of ale (though more on that later).
In any event, we can start our classification system at the "phylum" level.
I. We have two phylum of drinks: fermented and unfermented. What makes something fermentable and/or fermented? Fermentation is a biologic process whereby sugars are consumed by yeast and converted to alcohol (there are other products of fermentation as well, but for our purposes we only care about alcohol).
II. The classes of fermented drinks, for our purposes, are going to be grain-based and non-grain-based. Non-grain-based fermented drinks would include wine (grape and other fruit-based wines) and most liquors (though not grain-based liquors like bourbon and scotch and some types of vodka).
III. So within the grain-based fermented drink class we have a couple of orders: distilled drinks and non-distilled drinks. Distilled drinks are also found in the non-grain-based fermented drink order.
IV. Finally, we get to the family of beers. We could have a few other non-distilled grain-based fermented drinks, too - but most of those are temporary products in the distillation process.
V. Within the family of beer we have two genus based on the type of yeast that is used: top-fermented and bottom-fermented. We generally, though not always, call the first one an "ale" and we call the second one a "lager." Every species of beer will fall within one of these two genus.
VI. We can group the species within each genus into two sub-species based on the temperature at which the yeast is allowed to convert sugars to alcohol: warm fermentations and cold fermentations. For the most part, ales ferment at warm temperatures and lagers ferment at cold temperature. There are some beers however that use ale yeast but ferment at cold(er) temperatures - examples of this are the typical porter (though not the "baltic" porter, which, confusingly, is a cold-fermented lager yeast beer) , the alt-bier, and the kolsch. There are even some lager yeasts that ferment at high(er) temperatures to create beers such as a steam beer.
So, there you have it, the taxonomy of beer.