There are only a few different types of automotive batteries in use today: wet cell, AGM (absorbed glass mat), and gel cell. While the basic concept of the battery has not changed dramatically in around 100 years, the technology behind them has.
Your traditional wet cell battery is exactly that; wet. They come in two forms usually, serviceable and maintenance-free. The serviceable model allows for additional water to be added in order to replace that lost through evaporation or spillage. If you intend to go this route, make sure to check the dilution with a hydrometer prior to adding anything. Maintenance–free is well, maintenance-free.
AGM batteries and gel cell batteries have the sulfuric solution suspended in a silica solution and gel, respectively. While these do cost quite a bit more than a traditional wet cell, they do not discharge as rapidly, or build sulphation (that wonderful substance on your terminals) as quickly.
While most standard use batteries are 12 volts, there is also a 16 volt application that is mostly used for racing, and in some situations where an alternator is not used the additional voltage makes a difference. One caveat for the 16 volt battery use is that you MUST use a battery charger or maintainer rated for 16 volts as well. This also applies to the gel style and AGM batteries. Your typical wet cell charger can reduce the effectiveness of these batteries, and also lead to catastrophic failure (BOOM). Nobody wants that.