Kids can't legally drop out of school until a certain age. A 7 year old can't just decide to drop out and his parents can't just decide he doesn't need more school. Seriously, is compulsory education not a thing where you live? The police can actually physically pick up a kid that can't present a valid reason why he's not in school and cart him back there. Parents who don't make their kids go to school can be held legally responsible for it. For a young enough child that a parent failed/refused to enroll in school, the government can either force the parent to enroll them or take the kid to be enrolled.
I fully admit that the Circle isn't precisely like a school, but your earlier definition of "not being able to go wherever you want/whenever you want=prison" would also by definition have to include modern schools.
The state can't take my kid for missing too much school. Like I said if this were the case, school drop outs would be taken from their parents left and right. Moreso, if your kid is causing too much trouble, getting suspended a lot or something like that the school will kick your kid out. Even then the state won;t come and take your kid if you don't put them in another school.
As far as what constitutes prison. If you wake up one day all the windows are barred, all the doors are locked. Then some person says we took you from your parents because you were deemed to have a trait that makes you dangerous, you cannot leave here. Are you imprisoned in your house, absolutely. '
You could be allowed to still play video games, surf the net, talk on the phone, and you could have a tutor. Doesn't change the fact that you're a prisoner in your own home. If the guy tells you he'll kill you if you try to escape or that you have a GPS tracker implanted in you so they can track you down and bring you back should you try and achieve freedom or not come back when allowed to step outside, you're a prisoner. You're in the custody of whoever is holding you, not your parents anymore.