The OSP supply has four C-shaped rubber baby buggy bumpers instead of only two, so it's obvious that the sound of your recordings will have more "roundness" if you use this version of the product. (Not entirely joking--there really really are people who say that you can tell tube equipment will have a "warmer" sound because you can feel the warmth of the tubes, and that large-diaphragm microphones naturally sound "bigger," and so on.)
Seriously, the large majority of audio equipment sold on the semi-pro and consumer market today is mass-produced in the Far East, and while there are notable exceptions, the companies whose names are on the products are often little more than a name, a Web site and a bank account. I do wish that people would realize this; there aren't really 200 different microphone manufacturers in the world; three largely state-owned factories in China account for many dozens of brands, including some that aren't exactly low-priced.
So it's entirely possible that one manufacturer makes both products, and that they re-used parts of an existing product design to lower the cost of a newer one--it happens all the time. But if so, you still can't conclude anything about the innards from that.
People here might know of the ART "Tube MP"--a small, low-cost single-channel mike preamp that sells fairly well in some circles. Well, dbx sells an almost identical-looking unit which I took to be the same thing--until I opened them both up and found that they had entirely different circuitry. They were both terrible, but that's another story.
The point is, a factory may well re-use product packaging and/or circuitry to save a buck or ten, quite possibly behind the back of the companies whose names are on the product. And until you open up the actual items, you truly don't know what you have. And until you open up three or four of them from different shipments, you don't know whether you have the same thing or not, because they also make changes, sometimes without even notifying the U.S. or other company that's fronting for them.
--best regards