Originally EPs were usually 3 or 4 track 7"s.
When 12" singles came along, they were just called 12" singles, and were designed so that extra tracks or extended versions of tracks could be fitted on, so were almost always what you could call "EPs".
I think of an EP as a 7" single with more than 2 tracks on. A 12" single is a 12" single (that's just my own definition).
A mini album is whatever you think is too short to be an LP.
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