Not normally... ( though I have heard a few people use them as synonyms)
Normally, to me, a Test Double is more similar to a Stub. It allows the program to compile and run. It might provide some replacement behavior (a Test Double for an Email Sending class/service might log/store the emails somewhere for review, etc). But its not a Mock Object in the sense of setting expected calls and verifying that these calls were received as part of the test.