Places, counties and ZIP codes are three different maps of the same country. Using the wrong one is the most common data mistake.
The US has three overlapping geographies that people use interchangeably — and that is the source of most confusion in address and population data.
Incorporated places are legal entities with boundaries and governments. The Census publishes population estimates for each. A place can sit in more than one county, and a large metro area contains many places.
Counties are the main administrative division of a state. Every piece of land belongs to exactly one county (with a few independent cities as exceptions). Property records, courts and many services are organised by county.
ZIP codes are postal delivery routes, not legal boundaries. They cross county and city lines, and they change when the postal service reorganises delivery.
The free directories: US Places & Counties (2023 population estimates, county assignment) and US ZIP Codes (city, county, time zone, neighbouring ZIPs).