Summary
ref: link According to Kent Beck and Martin Fowler stories(User Stories) and features are SYNONYMS: A user story is a chunk of functionality (some people use the word feature) that is of value to the customer. What you call a feature is usually referred to as theme or epic. Themes and epics are used to group user stories to bigger feature sets, that make sense on their own.
From a more semantic point of view: feature is a part of the system you are trying to build, user story is a way to describe that part.
Correction:
As Pascal has pointed out - I maybe missed the real meaning of “feature” in that citation (“feature” obviously refers to functionality) Apart of this, I still think that one can use these words (feature and user story) as synonyms in a lot of contexts (“I’m working on this story” vs. “I’m working on this feature”), since, as Pascal said, a user story is a way to capture a feature. Which means there is a 1:1 relationship between those two. And, as can be seen from my remark about the semantics, this is how I really understand it.