What is the difference between a mid-rise and a high-rise building?

Firstly, there are no hard definitions.

Mid-rise: Between 3–10 stories. A lot of jurisdictions place the lower end at 6+ stories as most buildings can no longer be constructed primarily of wood.

High-rise: Usually 7 or more stories. A lot of jurisdictions place the lower end at 10+ stories. This is largely attributed to Chicago’s requirement during the 1880’s that any building 10 stories or more need a method other than stairs to reach each floor.