There are five major classes of game mechanics:
Physics, which are about the movements and interactions of simulated physical objects in simulated space. These don't have to be truly Newtonian; most games fudge their physics a bit to make the game more playable, and many games use what the industry calls cartoon physics.
Internal economies, which are about the construction, destruction, conversion, exchange, and flow of resources. In a shooter, the key resources are health, ammunition (of various sorts) and enemies (of various sorts).
Tactical maneuvering, which is about passing through and/or controlling space, typically in a hostile environment or in conflict with other forces doing the same thing.
Progression, which is about systems that control the player's march toward victory (or defeat). This can include the structure of spaces the player must navigate, i.e. levels, with locks and keys, but can also include stories the player must experience, or other kinds of missions or scenarios she must complete.
Social interaction, mechanics that facilitate interactions among players. Features such as auctions, bargaining, forming alliances, sending secret messages, or simple chatting are social interaction mechanics.
The book I wrote with Joris Dormans, Game Mechanics: Advanced Game Design, discusses these in more detail, especially internal economies. It also identifies a number of common design patterns used in internal economies. You can find out more about it here:


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