This came up in the comments, and as always The Weekend Pontificator is happy to tell everybody just what's what.
Champagne comes from the Champagne region of France. Sparkling wines from other regions of France and the rest of the civilized world are called "sparkling wine". In the United States, though, where anything that swims or just floats on the surface can be called "cod", and extruded vegetable oil and orange food color can legally be termed "something resembling cheese", you sometimes see "champagne" appropriated, usually for cheap, mass-produced dreck.
Sparkling wines are produced by taking advantage of the natural "secondary fermentation" that wines go through after the primary fermentation has stopped. The 17th century Benedictine monk Dom Perignon is often credited with "inventing" champagne. In fact he was a superb viticuleur who may have hit upon a combination of reinforced glass and a corking method which allowed champagne to be stored.
There are many ways to produce sparkling wines, the two major ones being méthode champenoise and the charmat, or bulk method. All true champagne and superior sparkling wines are made by the former. Secondary fermentation occurs in individual bottles which are then aged, generally for a minimum of two years. The longer the wine ages, the more CO2 is absorbed; this is why the mark of a good sparkling wine is tiny bubbles which are persistent. Good wines don't lose their sparkle in five minutes' time.
After the wine is fully aged, the bottles, which have been stored upside down to allow the sediment to fall into the neck of the bottle, are immersed in a cold brine bath, which freezes the sediment. The temporary cork is then removed, allowing the pressure in the bottle to shoot the plug of sediment out.
This is where the sweetness is determined. The bottles are topped off with a measure of still wine known as the dosage. Any sugar in the finished product comes from this topping off. Sparkling wines from the EC must be labeled according to their residual sugar. The rank, from driest to sweetest:
Extra-Dry (Extra Trocken)
Sec (Trocken, Secco)
Demi-Sec (Halbtrocken, Abboccato, Semi-Seco)
Doux (Dolce, Dulce)
The sugar levels actually overlap some, so the "Extra Dry" of one house might be drier than another's "Brut". Extra-Dry champagne is basically made for the American taste. Also, some producers make a sparkling wine with zero sugar, sometimes designated "Ultra brut" or "Brut sauvage" or some such.
The reason sweet sparkling wine is labeled "sec", meaning "dry", is that when champagne was first bottled the taste was for wines considerably sweeter than what we typically drink today.
The Weekend Pontificator recommends that you try drinking a little less for once in your hedonistic life and save enough to splurge on a really good bottle sometime. Veuve Cliquot Yellow Label is our favorite among what passes for reasonably priced champagne, and is superior to a lot of supposed "luxury" brands costing twice as much. Buy Moët et Chandon Dom Perignon or Roederer Cristal only if you're trying to impress someone with the label. If you must spend an obscene amount and want the best quality, buy Krug or Veuve Cliquot La Grande Dame.
Cheapo sparkling wine is just fine for making Mimosas or champagne cocktails. Asti Spumante, though sneered at by snobs like me, can be quite good for something gulpable.
More than you wanted to know? Then my work here is done.