TOPIC: Control procurements vs Closing project/phase

I'm a little confused at the difference between control procurements and closing project.
Control procurement includes closing out contracts in PMBOK 6th edition, but is also included as part of the 'administrative closure' of project in the Closing process on p.123.

'Control procurements' is a monitor/control process group but 'closing project/phase' is in the closing process. I've gotten a few questions from the exam simulator confused when it involves these two. For example, is 'finalizing open claims' part of 'close project/phase' or 'control procurements' or both?

I think a quick answer is this:

Control Procurements has to do with finalizing the procurements for sellers throughout the project. Say your project is to manage a project to build a house. You might have hired contractors for running conduit , building frames, pouring foundations. So you have loads of procurements that you’ll have to finalize throughout the project. The foundation might be poured Week 3 of a 20 Week project. You pay them (according to the terms/agreements) when the work is complete and accepted.

Close Project has to do with your customer accepting the house. Then you and the home owner close your stuff, after the deliverable is accepted and transferred. This isn’t the numerous procurements that went on during the building of the house.

Hopefully that makes sense. And hopefully that is right. Someone correct it if my understanding is wrong.

Also, that wasn’t a quick answer.

@Pazz Your answer seemed like a really great analogy. Like OP, I am currently studying to sit for the exam as well and have confused the two numerous times.
Could someone more "experienced" in what the exam is looking for answer Paz?
Note: I am aware this question is ages old.