Feel free to add your own descriptions with goals of objectivity and brevity.
Defense
Players need to defend against increasingly harder waves of enemies in one or more lanes. The goal would be to prevent enemies from reaching the end of the lane(s) or to kill enemies before a timer runs out.
Subgenres:
-Tower Defense (TD). Utilizes a mechanic where bunkers become invisible and does not obstruct construction of different buildings.
-Stacked. Utilizes a mechanic where a light switch (vision) can be toggled to allow buildings to be placed upon each other.
Helm's Deep
A PvP map genre based on the battle in the Lord of the Rings book and movie. Players control either an attacking or defending force. The attacking forces will successively spawn waves of units to breach the castle walls. The defending forces have a limited garrison and may include much stronger hero units. The defenders must hold out until the timer ends at which point reinforcements arrive and waves stop for the attackers.
Subgenres:
-Minas Tirith. Similar game play but is based on the later battle of the story.
Fastest
A map genre that maintains most of the vanilla melee features with the exception of stacked minerals and sometimes gas closer to a player's starting building. As a result players can harvest resources and advance through the game at a much faster rate without the need for expansions.
Mass
Players continuously spawn units within a single large area amassing huge armies to fight each other. Usually upgrades and/or different unit types can be utilized as well as a "massing" controller in which all the players units will be ordered to attack a specific location.
Subgenres:
-Zone Control. The arena is split into a checkerboard pattern with each controlled square spawning units.
-Evolves. Player units evolve into stronger units after a certain amount of kills.
Micro
A PvE map genre where players must control their small force of units precisely to defeat much more numerous AI enemies. Usually includes spellcasting, kiting, and abusing of AI behavior to overcome odds as the player units maintain their default stats.
Subgenres:
-Impossible. Players control a handful of units where they must kill enemies in a section of a map. Each map may contain several sections.
-Spire Defense. Similar to a defense map where players must prevent enemies from reaching the Spire at the end of the lane, however enemies can attack player units.
MOBA
MOBA, Multiplayer Online Battle Arena where two teams fight on 3 or more different lanes. Computer allies of each respective team continuously send units across the lanes whilst players control heroes which can push back these lanes and eventually kill the spawners.
Maps:
-Aeon of Strife. The originator of the entire genre, PvE. Based on the Starcraft lore of Protoss.
-Dynasty Warriors. Map themed on the Warring States period of China and the video games of its namesake.
-Temple Siege. One of the most popular maps of this genre.
Movie
Players are given no control and are effectively observers watching the events of the map.
Role Play (RP)
A sandbox map where players are given free reign to create their own stories. Usually has the largest map size with fully decorated terrain and a spawning section where players may spawn in most units.
Role Playing Game(RPG)
PvE maps where players progress through a story and map gaining levels and upgrades.
Snipers
Usually PvP map arenas where players must "a click" or manually attack other player units in order to kill in one shot.
Keywords:
-Paintball
Special Forces
Players start with a single unit and must clear out a map full of enemy computers. Players kill enemies for resources which they can spend on upgrades to allow them to face stronger enemies deeper within the map.
Test of Survival (TOS)
Players start with an invincible bunker and a small amount of Marines. The starting location constantly heals player units but they can be damaged enough between healing intervals to die. Computer enemy units fill the map and will occasionally attacking the starting area. Players must upgrade and make more units to eventually clear out the map.
Very Hard CPU
PvE map genre that mostly maintains normal melee gameplay but has AI that is more aggressive with infinite resources. May contain fastest map elements. Common arrangements are 7v1 and 5v3.
None.