In many cases, there is only one part number for a particular tire in a particular size. If that part number is used at the OEM level, then what you buy at Costco is the exact same tire that gets installed at the factory.
The Primacy MXV4s on our MDX are the OEM tire on the Honda Odyssey. P235/65R17; there's just one SKU (66126). Michelin doesn't make a 66126-1 that gets shipped to the Lincoln, Alabama, plant to be installed on new vans, and a 66126-2 that goes to the aftermarket distribution channels. It's the same tire.
Michelin's website used to offer a very nice and easy-to-access full spec page for each tire, showing the part numbers, the speed ratings, the OEM applications (if any), for each size of any one model. Since they re-designed their site to be mobile-friendly, that seems to have gone away. You can still find these details, but you have to look tires up by size. The LTX M/S2, for example, in P265/60R18, are OEM on the Toyota Tacoma. They're SKU 39274. If you buy this tire from the aftermarket, look at the SKU you're buying:
https://www.tires-easy.com/265-60-18/michelin-tires/ltx-m-s2/tirecode/39274
https://www.amazon.com/Michelin-LTX-All-Season-Radial-Tire/dp/B01DJXL0M6
http://www.tiresupplysc.com/browse/tires/Michelin-6/LTX-MS-2-19820/P26560R18-148936
https://simpletire.com/michelin-265-60r18-39274-tires
http://www.kauffmantire.com/tire/M39274.html
If you can find a Michelin LTX M/S2 in P265/60R18 size that has a different Michelin part number, that would be very interesting indeed!
Another example: Michelin Premier LTX in P245/60R18 is OEM on the Lincoln MKX. SKU 62570. Can you guess the part number of the Premier LTX in P245/60R18 sold at Costco? I'll give you a hint...
http://tires2.costco.com/product.aspx?It...2b-ee490a985daf
There are some cases where there are multiple part numbers for a tire in a given size -- one (or more) used at the OEM level, and perhaps one used at the aftermarket level. To be frank, I personally see less and less of this. If a manufacturer is already making a contract tire for the factory, that's probably the exact same version they're shipping to distributors. This is very evident with GM tires -- you can see the large "TPC" number branded on the sidewall, a GM requirement.
http://www.mycertifiedservice.com/tire-sidewall.html
It's very common to see a tire sold at a Goodyear or a Michelin store with the TPC number -- because it's the very same version as the one installed at the GM factory. I think tire manufacturers see efficiencies in building just one version of a specific tire model and size. Consumers often don't know the difference.
I think both statements can be true at the same time. An OEM tire is indeed formulated and built differently than the same tire otherwise would have been if it wasn't being made under contract. At the same time, what you buy at Costco or Tire Rack often IS the very same tire as what gets shipped to the factory, because the tire manufacturer isn't making a dedicated "aftermarket" version of that specific tire in that specific size.