For example we are talking about special machine vision optics, cheaply manufactured by a chinese company, exclusively made for a well recognized western company with a brand name. The manufacturing process accords to strict standards assured by frequent audits by the said company, but the manufacturer is not withheld from selling the products elsewhere in general, but they must not either sell it with the western brand name, nor to any branded reseller. So one can actually directly buy from the manufacturer, without the "Western brand optics" label on it, but the product is exactly the same.
I would say it is "OEM", but in my perspective it would mean that the manufacturer does sell the products for other brands too, with different labels... but it does not: it either puts one specific label on it and ships to the western warehouse, or sells the products under no specific name "under the counter" on e.g. Aliexpress.
Is there a separate word for these products? I tried googling and inventing word combinations, but I did not find one suitable word/acronym. Should I just say OEM for this too?
Thank you for all ideas!