I might be misunderstanding your questons, but I'll give it a try:
In the case of hotel reservations, reservations exist within the hotel's own, proprietary systems. An individual traveller's Personal Name Record (PNR), whic resides on the GDS vendor's system, will have references to the hotel confirmation number, but the reservation itself stays on the hotel provider's system.
The hotel companies provides "programming interfaces" that allow the individual GDS vendors to tap into the hotel company systems. The hotel companies have the ability to provide so-called "last room availability" to some GDSs and not to others - it depends on their individual agreements.
Lastly, there is a different kind of interfacing, known as "accounting interfce" where the PNR information from one GDS is introduced into the 'back-offce" system provided by a second GDS vendor, but I don't think that this what you have in mind.