No it is better to separate the two concepts :
Acceptance Tests define exactly what the system has to do before the customer will consider it "Done".They don't just include functional requirements; they also test the non-functional stuff like performance, security, and useability. If functionally is not covered by the Acceptance Tests, it's not required by the customer.No story or feature can be said to be done until the suite of acceptance tests that define it are passing.
User stories are short, simple description of a feature told from the perspective of the person who desires the new capability, usually a user or customer of the system. They typically follow a simple template:
As a <type of user>, I want <some goal> so that <some reason>.
Below a couple of links for further readings :