Two basic windings; Flatwound and roundwound.
Roundwound strings are more growly, mid oriented with expressed treble. They are exceptionally more "raw".
There are 2 basic types of rounds- Steels and nickel coated. Steels really emphasize the upper mids and have a lot of rich overtones. They tend to be rough in texture though, some people don't like that. Of course, some aren't too rough.
Nickels are more "warm" than steels, emphasize the lower mids and are nicer to the touch.
Flats, as opposed to rounds, emphasize on the base of the tone. They are used to get that "thump" mostly. They feel nice to the touch as they are nice and round.
All strings can be either hex or round core. Round core is more flexible, has less tension, hex has more tension and is less flexible.
Here are some sound clips of different rounds and one set of flats, that should be good to get you going.
[Invalid or Expired Link Removed]