Many subwoofers have tricks to gain control over this problem. Velodyne has a device called an Active Servo Control that uses an extra magnetic field to control the subs behavior. M uses a second vented driver to make sure that the first doesn't lose control. For this reason, it is difficult to judge a sub by it's statistics alone. That is the purpose of the table at the bottom of this article.
Name does matter a lot of times.
A subwoofer can be set up a number of different ways. It the most popular configuration it can handle all the base from all five channels, thus letting those channels only handle signals roughly 80 hz and above. This works best with bookshelf or satellite speakers which can't properly reproduce lower signals. With a system that has tower speakers, it can work in conjunction with the base from those speakers, or handle the base for the center and surrounds if they are still smaller speakers. With Dolby Digital, the specs call for a full 20hz to 20khz on every channel, and 20hz to 100hz on the LFE channel.