OE vs OEM parts are they even same?

[mikkhh]

I understood that OE part is Original Equipment manufacturer let's say in the red engine case cmmins itself. And OEM is Original Equipment manufacturer for in this case let's say filter or bearings manufacturing company.

But what about the parts that new engines are assembled from VS the replacement Original Equipment part that you buy at dealer? Is there some quality difference to be expected?

What is the story with old part core charge being same on NEW or reman part? The local dealers are just trying to screw over customers?