TOPIC: Control Procurement(Procurement management) Vs Close project or phase(int. man)

Can you please explain me the relation ship between control procurement which is performed by buyer and close project or phase (integration management) which is performed by a seller PM.

As per my understanding , when buyer does close procurement in control procurement process , Close project or phase process simultaneously takes place i.e. Buyer sends confirmation to seller that contract is complete and seller PM does project closure activities.

Let me know if my understanding is right.

Thanks,
Vivek