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:
To answer “How scrum works,” most of the teams I've worked with first addressed the question: “where to start?” That question applies to both implementation and improvements on the Scrum framew...
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