Examples of games that use 3D graphics on a 2D plane:

It is worth noting that games of this type do not have to be completely flat. For instance, in Klonoa: Door to Phantomile, although the player model is restricted to a 2D plane, the plane itself can curve through three dimensions as the platform you're running along twists and turns.

Examples of games that use 2D graphics to create an illusion of 3D:

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