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:
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Planning and grooming sessions all come with their own sets of rules. Team members meet to estimate stories or other work items, all according to an agreed-upon process. And with every session comes ...
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