According to [this wiki page][1]:

**Survival**

 - Intended to encourage cooperative play.
 - When players die, they become [ghosts][2].
 - Ghosts cause the sanity of living players to drop if they are nearby.
 - Ghosts can be revived by certain items.
 - When all players die a timer starts. If nobody revives themselves before the timer is up, the world resets and all players start anew.

**Endless**

 - Intended to be more relaxed and casual.
 - When players die, they become ghosts.
 - Ghosts have no effect on the sanity of living players.
 - Ghosts can be revived by the same items as Survival, but also at the [spawn portal][3].
 - Even if everyone becomes ghosts, the world never resets.

**Wilderness**

 - Intended to be more like other survival games.
 - Players spawn in random locations.
 - When players die they do not become ghosts. 
 - Dead players lose all their items and map information, and respawn at a new
   random location.

  [1]: http://dont-starve-game.wikia.com/wiki/Don't_Starve_Together
  [2]: http://dont-starve-game.wikia.com/wiki/Ghost_Players
  [3]: http://dont-starve-game.wikia.com/wiki/Jury-Rigged_Portal