ECM PNs vs OS PNs

I put this question on the "Scanning" section of this Forum; maybe it should be here instead:

I'm new to this DIY ECM tuning world and I'm trying to understand how to identify OS PNs that are compatible with a particular physical ECM PN. Example: I have a PN 12617630 ECM supposedly (did not see the donor vehicle) from a 2008 5.3L Silverado 4WD w/the factory OS. I've seen online references to an E38 OS PN 12617631; would that likely be the factory OS that's in this ECM? Is there any known standard PN relationship between the ECM PN and the factory OS PN it uses? I'd like to understand how to determine ECM vs OS compatibilty

Unfortunately probably GM is the one people that would have a comprehensive parts listing like you are after.