Partially quoting myself from previous answers to similar questions:

Most societies have had people who's duty was to "keep the peace" so to speak.

In Ancient Greece, for example, city states had publicly owned slaves who acted as a police force. They kept order and controlled prisoners, but they didn't investigate crimes. Most crimes were considered a private matter so the citizens dealt with them themselves.

The city of Rome never had a real police force, though it did have a force of men set up for the protection of each ward. These men were responsible more for public order and physical protection and had no role in criminal justice.

Medieval European cities had forces along these same lines. For example, the duties of Lieutenant General of Police, the foundation of the Paris police, were described as "ensuring the peace and quiet of the public and of private individuals, purging the city of what may cause disturbances, procuring abundance, and having each and everyone live according to their station and their duties".

The thing to keep in mind about criminal justice as a whole is that, for most of history, crimes were considered private matters between individuals. With crimes being private matters, there was no impetus for the state to provide police as we know it today - they only needed a force that could keep order. Eventually a new idea took hold in England: violating the King's Peace (through murder, theft, etc.) was not just a crime against an individual, but a crime against the whole kingdom. This brought about the prosecution of criminals even when no private citizen brought a case against them.

This eventually led to organizations like London's Bow Street Runners, founded in 1749, who are regarded as the foundation of modern police. They were a formalization of the existing practice of 'thief-takers' - people who solved crimes for a fee. Then, in 1829, in response to the growth of London (and the growing difficulty in keeping the peace) the Metropolitan Police Service was established. This was the first professional, modern police force that was built as a civilian service, with civilian oversight, and accountability to the people.

So the idea of "city guards" is, on the face of it, fairly accurate. There weren't police, as we know them, only a force of men set up to prevent riots, keep unwholesome people out of the city, and maintain order.