I thought maybe I'm just dense because I couldn't keep straight who was the OEM and who was the rebrander. Not which company did which but which was the "OEM". Common sense would seem to indicate the OEM was the original manufacturer, but I've seen rebranders referred to as OEMs. So I did a little digging and found this:
OEM (original equipment manufacturer)
This confusing term has two meanings:
1) Originally, an OEM (original equipment manufacturer)REG was a company that supplied equipment to other companies to resell or incorporate into another product using the reseller's brand name. For example, a maker of refrigerators like Frigidaire might sell its refrigerators to a retailer like Sears to resell under a brand name owned by Sears. A number of companies, both equipment suppliers and equipment resellers, still use this meaning.
2) More recently, OEM is used to refer to the company that acquires a product or component and reuses or incorporates it into a new product with its own brand name.
Also see value-added reseller(VAR), a similar term applied to the repackaging of software.
Clear as Mud?