Although you may hear the terms “seismic zone” and “seismic hazard zone” used interchangeably, they really describe two slightly different things. A seismic zone is used to describe an area where earthquakes tend to focus; for example, the New Madrid Seismic Zone in the Central United States. A seismic hazard zone describes an area with a particular level of hazard due to earthquakes. Typically, a high seismic hazard zone is nearest a seismic zone where there are more earthquakes, and a lower seismic hazard zone is farther away from a seismic zone.
There was also a seismic zone system (0,1,2,3,4) used for building codes that is now obsolete. See the last question here: Earthquake Hazards 201 - Technical Q&A