In theory, persons refers to a finite, countable number of individuals and people relates to large gatherings, ethnic groups, or the overall population. However, people has been used enough as the plural of person that that definition has also become valid. These days, the distinction is only ever made in legal and formal contexts.
Everyone has seen signs in elevators, taxis, and elsewhere that put a limit on the number of “persons” allowed at a time. You may also have heard of “displaced persons” and “missing persons”. If you’re anything like me, you’ve wondered why they never say people.
Currently, the word people is almost always accepted as a plural of person. Aside from legal situations, no one is going to correct you if you use people when describing a countable number of individual persons. But it wasn’t always that way. In fact, the words originated from two separate latin words with completely different meanings.
Person and people both derive from Latin, but from different words. Person came from persona, which first meant “mask,” like that worn by an actor, but eventually came to mean “an individual human.” People, on the other hand, came from populus, which means “the people” in the sense of a group from the same nation, community, or ethnic group.
While the original definition of persons has been almost entirely adopted by the word people, people is still sometimes used to describe a single ethnic group or national population (“a people”, singular) in terms like the Canadian People or Indigenous peoples.