OE is BMW.... It is the one definition that retains meaning.

OEM can mean anything: classically the "M" refers to the maker (ie Manufacturer)... in common use (your use) it can be used to signify the original equipment item... but it is also used to mean "identical item made by the same manufacturer that made the OE part, just private label"..

It has been corrupted to apply to "almost any part as long as the manufacturer once made a part for a OE business somewhere, maybe not your particular the car".

Sadly it has become a distinction without any meaning or value.

You can insist "I want OEM wheels" and you might find yourself with copies of a BMW wheel from a company in Pakistan that makes OE wheels for their local car company.

If you really don't care about the quality of the wheels, then ebay is a fine place to buy. Once you move from "a manufacturer with something to loose if they screw up a casting", to "a cheap 3rd world knock off with no capital and no traceable ownership" your risk rises.

IMHO

A