Can you purchase from the app store with someone else's appleid?

Question

My grandson has his own iPhone.  He uses it to play APPS.  He has his own AppleID.
His father downloaded a new game using his own AppleID onto his son's iPhone.
My grandson's iPhone now seems to be confused as to what AppleID it belongs to?
When an AppleID is created, I assume Apple set it up so the AppleID is a one to many relationship.  That way
you can have multiple products using the same AppleID.
Does the MAC Address of the device the AppleID is created on get stored and referenced when interacting with
The APP'S Store?

Answer 1

On the iPhone, open the App Store app, go to the Featured pane, swipe to the bottom, tap the Dad's Apple ID and sign out. Tap again and sign back in with Son's Apple ID.
If it won't change the Apple ID you may be encountering the fact that an iOS device can have the content of comingled Apple IDs synced to it from the libraries of the iTunes app on a Mac or Windows box, but unfortunately, an iOS device itself can only have one Apple ID associated with it every 90 days. That may be what you are encountering, Dad has signed into his Apple ID on Son's iPhone and the lot of you are stuck with that for 90 days, after which Son may again sign into his Apple ID on the iPhone.