If you're fermenting grains, it's beer.
If you're fermenting fruits, it's wine.
If you're fermenting honey, it's mead.
It's not really that simple, because there are beers that use fruit (e.g., cherry lambic, raspberry wheat), beers that use honey (it's a fairly common adjunct), wines that use fruit (e.g., elderberry wine), and a whole lot of meads that use fruit. The crossover is substantial. When you consider hard ciders, it gets even more complicated (is apple wine really a cider?).
The base ingredient of beer is almost always malted barley. Even beers named for another grain — like wheat beer, oatmeal stout, rye beer — use malted barley as a base. Hops are a critical ingredient in beer for two reasons: bittering and aroma.
The base ingredient of mead is always honey. I've had mead with hops (Charm City makes one), but it's uncommon, and I personally don't like the flavor.
It's more common to find a winery that makes mead than a brewery that makes mead. There's an outstanding one in Montana called Hidden Legend. They also make a mead/wine blend called a "pyment," which was popular in the 15th century or so.