Guns alone cannot do what I’m describing. A person wielding a gun can contribute to a prison.

Either the gun itself or a person wielding a gun, depending on what exactly you mean by "subjugates", is the prison. If at the very least a person with a gun doesn't qualify as a prison, then it follows that a person with a gun can't subjugate a "criminal".

Neither would I, that’s just executing someone.

But it's (a) an instrument which is inherently violent (b) an instrument that can subjugate criminals and ( c) is used by the ruling class to do so. So what's the difference?

I would consider physical harm or withholding necessities to human life to be violence. The constant use of these are a core component of prisons. Schools, hospitals, re-education camps, etc. all include the threat of violence if someone does not comply, but the institution does not require violence to function.

So if a criminal is locked in a cell, but not otherwise harmed, they aren't in a prison? Or is being locked in a cell inherently violent?