Zoning designations means different things in different jurisdictions. Each come with their own use limitations, height and setback requirements, minimum yard requirements, open space requirements, and the like. There may also be sub-categories from more specific contextual zoning districts.
In New York City, R3 zones are low density residential districts for one and two family attached and semi-detached homes, and also for medium density general residences like garden apartments (depending on which sub-category you are inquiring about).
Consult your jurisdiction's zoning laws for a definition of a particular zoning designation. Also, be sure to check out any other definitions used within that definition. If you really want to delve deeply into zoning, consult a city planner or a local architect / engineer with knowledge of the area.