Rarely does a game pop up that does not involve a character ordering mead or beer or some other such drink. I've never really taken the time to understand the difference between the two, and on the off chance that you have not either this seems like the perfect place to blather about it.
Turns out mead, called honey wine as well, is a drink concocted from honey and water. The two are mixed and allowed to ferment. The concoction can be flavored with various fruits to give it a slightly different taste. So you might have apple mead, or grape mead etc. Hops can also be tossed in in order to make a beer-like taste to the mead. Mead is generally clear, with a slight tint to it if flavored. I would assume mead is the cheaper of the drinks and is available at most boards, whether in the morning or evening.
Beer comes from cereal, barley or wheat that is mashed with hot water; this process allows the sugars to break down which creating what is called sweet wort; the wort is separated from the grains, boiled often with hops thrown in for flavor and then the whole mess allowed to ferment. (I suspect I've left something out here). Beer is the younger of the two liquids and by far the most complicated to make. I suspect it would cost a little more than mead.