Epics should be used when you want to group a bunch of issues together for visibility and easy tracking of percentage done. Think of it like a traditional project level grouping where the project has a defined start and end date.
We typically do not use story or task but create our own issue types because Story and Task are too generic for the work we do and it makes it harder to get metrics.
Here's an excellent blog by Mike Cohn on the differences between Story and Task:
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