A smart proxy interposes additional actions when an object is accessed. The Proxy provides a surrogate or place holder to provide access to an object. A check or bank draft is a proxy for funds in an account. A check can be used in place of cash for making purchases and ultimately controls access to cash in the issuer's account. Adapter provides a different interface to its subject.
Proxy provides the same interface.
Decorator provides an enhanced interface. Decorator and Proxy have different purposes but similar structures. Both describe how to provide a level of indirection to another object, and the implementations keep a reference to the object to which they forward requests.