John, good point.
Take Hikvision and IC Realtime.
Hikvision is the 'original equipment manufacturer' and IC Realtime is the rebranded / re-seller.
But, in common usage, IC Realtime is the OEM and Hikvision 'just' the manufacturer.
If it helps at all, the way I remember it (possibly wrong) is like this:
Many years ago, O.E.M. meant exactly what it stood for Original Equipment Manufacturer.
Then at some point people started describing the action of utilizing OEM's with the clusmy infinitive, OEM'ing. As in: Ruthless Retailer is OEM'ing their whole line of Wacky Widgets from Major Manufacturer.
Maybe because the of the awkwardness in pronounciation, eventually the 'ing' part started getting left off more and more. And it on the surface it seemed logical, since if you are OEM'ing you must be an OEM, just like who ever is dancing is a dancer. But still most people weren't confused about it. You just knew what was meant, but more and more it referred to the rebrander, not the manufacturer.
And finally a new group of people have entered the workforce who are familiar with only the second usage. Leading to the seemingly opposite dejure (Manufacturer) and defacto (Re-labeler) definitions.
Now the way I think of it is context driven, like 'Aloha' or 'Shalom'...
I would guess that the confusing change of meanings is deliberate. Although many companies buy their products from others, most either don't admit it at all or try to hide the fact - often by claiming they either designed the products (typically just picking from a menu of options offered by the true manufacturer) or that they perform final assembly/inspection/QC/packaging.
I experienced a good example of that when trying to duplicate Pelco's CCC1300-series of small box cameras. Pelco discontinued the line and replaced it with their C10-series, which was a bit larger and provided a whole lot poorer picture quality. Through a series of frustrating web searches, I was finally able to determine that the original manufacturer was Fujitsu but neither Pelco nor Fujitsu would admit it - Pelco would not comment and Fujitsu just said they only sell through other companies without supplying any names.
Someone at Pelco finally admitted Fujitsu was the source long after I gave up and found another brand of small cameras, although I haven't found any as small as the original.
I also think the whole thing is at least indirectly related to the "Buy American" BS. U.S. companies can claim their products are American (wink, wink) by performing the minimum processing necessary to qualify for that designation.
John H. you're Linked In reply to "LTS Genuine Products" prompted me to rethink this topic. Looks like not much has been clarified in the last 4 years.....