Nonlinear play is the middle ground between linear and sandbox play. It may be somewhat restricted, such as by geography or tests, but allows for a significant amount of player choice in how it is played. Nonlinear games often use combinations of levels and spaces for their geography.
The term is commonly used informally to describe games which have high optimality. Deus Ex, for example, has many levels which can be solved in several ways and so its play is nonlinear. However the game world is not totally open, unlike a sandbox game. Real time strategy games often make heavy use of nonlinear play.
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