Today, in most Western states, the local police force and the military are separate organizations with different missions and agendas. Generally, just by looking at equipment and uniform, a local can determine whether someone is military or police. I’m wondering whether this distinction would’ve existed in the Roman Empire (any period).

Would those conducting internal security within domestic territories like the city of Rome itself be distinguished from soldiers in terms of chain of command, dress code, or mission? Or would the “police” force be just another military branch, or perhaps a temporary assignment for soldiers?