Are all buildings required to have a sign showing the maximum occupancy?

Simple answer; no.

For the most part, only rooms where people are expected to gather for some length of time. This number doesn’t represent the actual amount of people that can be packed into a space, but the amount of people in the space at a predefined density. It is to be used as a guideline for fire safety as the space was designed to get at least that many people out of the space within limits set by national fire safety guides.