Not at all..
A user story represents small parts of business value.
So it is really difficult to say when an user story is a subset of a feature or a feature is a subset of a user story (also keep in mind that the user stories are usually written by the stakeholders, which tend not to know exactly what they want ... :) )
So, if you follow the recommendation of agile to keep the stories short you would fall on the "best" scenario that is the user story being a subset of the feature.
However if your stakeholder write long stories, each story would have a couple of features ( if there is a good communication between the team and the stakeholders this won't happen since the team will break the stories into small ones)
