We'll keep it brief—

Legislators work together as part of a governing body to propose, debate, and vote on laws and policies.

Executives can sign laws into effect (or veto them) and are responsible for carrying out and enforcing those laws by issuing regulations via executive branch agencies.

Quick Judicial Branch refresher —

Judges interpret and apply the law. In other words, they decide how laws impact real life disputes. Judges also review whether laws and government actions follow the state constitution.

Cities and counties are different levels of local government — Ann Arbor is a city inside Washtenaw County.

In Michigan, the city handles day-to-day services, like: transit, housing, and police & fire departments. 

The county manages systems that serve multiple cities and townships, like: courts, health care, and certain public records.