I'm confused by your statement. If "Ban != Access" then what's preventing courts from simply denying access (not a "Ban" under your assertion above) to people outside of prisons as well?

My thinking was same as the parent. Preventing access would involve telling someone who owns a computer and could, for example, connect to public wifi, that they are not allowed to do that and will be punished for doing so.

I think this would be relevant to someone who has committed a crime using a computer and remains banned from using the internet even after finishing a prison sentence (like the kid in the movie Hackers). It doesn't sound like that can happen now.

Suppose a state doesn't bother to install an internet connection in the prison, and confiscates phones with mobile data. This is denying access.

Suppose someone is caught with an internet phone in jail and is hauled in front of a judge. If it's banned, then they can have their jail term increased.

Yea I understand the "If you're in prison" side of this but I feel like asserting "Ban != Access" makes the general public (i.e not in prison) side of this MUCH fuzzier.

What's the difference?

Cigarettes aren't banned. That doesn't mean everyone gets free cigarettes.

I can't stop you from going online but I don't have to give you a computer to access it?

Again what's the difference? Your actions forbade someone from using the internet, what's the difference besides playing dumb word games?

You can get some money together, go and buy a laptop, connect to free public wifi. The government cannot ban you from using it if you complete those steps. i.e. they cannot be the only thing preventing you from accessing the internet. If you have no money or no way of buying a computer or no way of accessing a connection that's on you, the government isn't required to give you those things for free. Huge difference between the two concepts and very much not word games.

I'm pretty sure US prisons don't allow you to have a laptop (they certainly don't permit cell phones), nor is there likely to be public wifi on the premises.

I'm not sure how you can't see the difference. If you have a laptop + Internet subscription you can access the internet. If you don't, tough luck.

"Access to the Internet" is the right. Not the tools to access the internet.