Answer:
They are not as they both have the same features it just provides a better understanding when using one diagram in conjunction with the other.
State machine diagram shows how state of some object or system could change, so transitions on the diagram are from one state to another state.
Activity diagram shows set of actions and how one action could lead to another.
In simple cases these diagrams might look like reverse of each other but in practice you need to select whether the diagram is about discrete number of states of some object or is it about organization of actions and activities possibly related to many different objects.