Differences between Proxy and Decorator Pattern

The real difference is not ownership (composition versus aggregation), but rather type-information.

A Decorator is always passed its delegatee. A Proxy might create it himself, or he might have it injected.

But a Proxy always knows the (more) specific type of the delegatee. In other words, the Proxy and its delegatee will have the same base type, but the Proxy points to some derived type. A Decorator points to its own base type. Thus, the difference is in compile-time information about the type of the delegatee.

In a dynamic language, if the delegatee is injected and happens to have the same interface, then there is no difference.

The answer to your question is "Yes".

Decorator Pattern focuses on dynamically adding functions to an object, while Proxy Pattern focuses on controlling access to an object.

EDIT:-

Relationship between a Proxy and the real subject is typically set at compile time, Proxy instantiates it in some way, whereas Decorator is assigned to the subject at runtime, knowing only subject's interface.