The summary of MEANS OF EGRESS:

Egress means go out or leave. In architecture, it related to an EXIT.

Building codes specify the security systems and its facilities, and it also specifics the Exit Accesses: the  max and min distance to them,  the amount of them,  some equipment around them, such as emergency light and clear sign, and discharge place, all of them must meet the building codes.

In the reading STAIR DESIGN, the author tell our some specific detail of the dimensions of risers and treads in a stairway.

In the reading STAIR REQUIREMENTS, describe some detail information: the Guardrails, the  Stairway Width, the landings, the Handrails, the Treads, Risers, and Nosings, and some other relatived details.