What is the difference between Adapter, Facade, and Proxy?

Adapter changes an interface so an incompatible component can be used by a client. Facade simplifies access to a complex subsystem by presenting a higher-level interface. Proxy controls access to another object while generally preserving its expected interface.

All three are structural patterns, but their intent differs: Adapter is about compatibility, Facade about simplification, and Proxy about controlled indirection.