Minecraft wiki entry for Creating_a_challenge_map, associated text: Adventure
A challenge map made for players that go on an adventure in order to accomplish some goal. Most of them have the /gamerule keepInventory to true to make it easier. E.g.: Zombie apocalypse maps.
Parkour 
A map that's just made for parkour.
Survival 
A survival world that is changed to make survival more difficult, or easy. A good example is the Skyblock map.
Puzzle 
A map that's made for puzzles.
Game 
A Minecraft mini-game, showcased in the form of a challenge map.
PvP 
Maps made for PvP.
Arena 
An arena with mobs spawning that you must defeat.
Dropper 
A type of map when you need to survive falls in style.
Capture The Flag 
A type of PvP, but the goal is to capture the other teams' flag(s)
Minigames 
A map designed to have many different and random minigames that players can play.
Role-Play (RP) 
RP maps are simulation maps that are related to jobs or situations in real life. These maps are best to be played in multiplayer.
Tycoon
Tycoon games is where you have some type of money-making machine, which you can upgrade over time to produce more money. You can use that money to build specific things in your map. For example, If the tycoon is a building, then you need to save (not actual price) $5,400 to build it. You know when a tycoon is finished when all the land plots are bought, and the map is filled in.