An Epic will incorporate a larger body of work, big enough to need to be broken down into Stories. So the basic difference is in hierarchy, where an Epic is the most general type, containing of multiple, more specific Stories, and eventually (optionally) Sub-tasks of Stories, which describe and track the work on the lowest and most detailed level.
EPIC vs Story is more towards a methodological question. If you like to understand more about EPIC and Story in Agile methodology, you can review this article here including a brief example:
G’day everyone! Super exciting news coming from the Marketplace. We have now fully rolled out the ability for end-users to submit app requests to admins directly from within the product! No longer ...
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