I can only speak for the UK and from a amateur perspective but here’s the rough breakdown:

90% of the time it’s likely a private pilot that’s wandered into a restricted airspace without realising it. They’re politely escorted out.

9.9999% of the time is an adversarial nation testing the response time of the quick-reaction force defenses. They’re politely but forcefully escorted out. Maybe some insults traded over the radio but that’d be about as heated as it gets.

0.0001% they pose a threat and refuse to be escorted out. At that point it’s basically the same thing of asking “what would happen if someone climbed the fence to the White House and towards it and when the secret service pointed guns at them didn’t stop, would they get shot?”

It’s the pilot’s call at that point, but if they posed a threat to life then yes they probably would shoot them down.