I am a library director and we have security guards in our building, so I can speak from that perspective:

Unarmed security guards have very little power. They can intervene in a situation and provide peace-of-mind to the staff member by standing by when a security incident takes place. They are allowed to physically touch a person and remove them from the facility if they determine that person to be a physical threat to others (or themselves). This is not considered battery because they are allowed to "diffuse situations by removing any one from the building" based on their assessment of the situation.

Interestingly, if the person being physically removed from the building acts accordingly and tells the guard to "stop" and proceeds to exit the building under their own power, the security guard MUST stop touching them. This rarely happens, however.

A patron is under zero obligation to stay put if a security guard detains them. In other words, the guard does not have the power to arrest people, so if a guard yells at someone to "stop" or to come back into the building for questioning, the patron has every right NOT to comply with that order. Even if the security guard tells them that the police are on their way, they do not have to stay.

Once the police arrive, it is a whole different story.

Also, a patron is under no obligation, nor is there any penalty for, providing no information, false information, or whatever. It amazes me how many patrons willingly give up their information because there is no law that says that they must comply with the guard's wishes. The guard is there to protect the employees, not to detain and arrest people.

If a patron is assaulting a staff member, a security guard is able to physically stop them, but I would draw the line at "attacking" the assailant. The whole idea is to diffuse the situation as quickly as possible, and a guard does not have the right to fight someone.

If the guard attacks a patron, the library assumes no liability, because they are contracted employees. The company that we contract with is in trouble, not us.

The guard is afforded a BIT of leniency when it comes to the law regarding battery, because they can remove patrons by forcing them out of the building. If a lawsuit arose out of such a case, we could prove that the patron was acting in a belligerent manner and that they committed several crimes before being escorted out. That puts the defendant in a tough position to argue battery.