I will list here modes and maps for shooters that we think of in a mini-database. This is meant to be constantly evolving, so contribute ideas and settle on clear names and definitions.

GAME MODES
Name: (extra info) goal_game-play notes

Assault: (Brink's current only and default game mode) Complete one or more goals of varying style in a linear fashion, one at a time_ this game mode can be seen as early as Unreal Tournament from 1999.
Conquest: (Battlefield 2 illustrates this game mode perfectly as its default game mode) Stay a specific distance from one of at least 3 points which are scattered around the map in order to capture them_ capture rate may be instant as seen in Unreal Tournament 1 or slow and only require being near instead of touching the point as seen in battlefield 2.

Last Stand: (Oldest and simplest mode ever conceived) Survive increasingly difficult waves of AI-controlled enemies as long as possible_enemies may increase their health, numbers, damage, arsenal of abilities, or other things, and this game mode is seen in flash games predominantly and has been around for a long time.

Deathmatch: (Doom of course) Kill all other players in order to obtain the most kills

Team Deathmatch: (none) At least two teams of players kill each other to gain more kills than the other team(s)_It's a common misconception that two teams is the right number for this. Technically, a free-for-all is a team deathmatch with a number of teams equal to the number of players.

Squad Deathmatch: (Wingman in Gears of War 2 illustrates this partially) Same as team deathmatch with gameplay changes_ Teams are limited to a certain number of players. If a team is full, players are put on a new team. example: teams of 4, with 15 players on server would have 4 teams. 3 would have 4 players on them, and one would have 3 players.

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MAP STYLES
Name: dominant play style(s)_non-dominant play styles

Open: sniping_rushing
Maze: rushing_sniping

add more ideas!