What is the difference between a User Story and a Feature in Agile terminology? [closed]

I guess a feature could be something like "credit card authorization", while a user story may be "authorize credit card for paypal".

So, is a user story a subset of a feature?

Yes, something like a subset. This article is a good read:
Features vs Stories

Excerpt:

I realized today that I hadn't made explicit the difference in my mind between features and stories and it's an important difference. Essentially, a feature is a group of stories that are related and deliver a package of functionality that end users would generally expect to get all at once. For instance, inline table resizing is a feature (note: this is the ability to drag to resize tables, rows and columns – try it in Word). In the first pass, you'd probably have a single story for inline resizing of tables, but it would be too big to estimate. So you break it down into three stories, resize columns, resize rows and resize the table itself.

According to Kent Beck and Martin Fowler 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.