What’s the difference between people and persons? The fast-and-loose answer is that people is correct and persons is wrong; the former word has supplanted the latter as the plural form of person.
At one time, the distinction between the terms was that people is a mass noun referring to an undetermined number of humans (“I’ve known a lot of people like that”), while persons is employed when the quantity is known (“Seven persons were apprehended”). Persons is still appropriate in legal and other formal contexts (“Authorities are seeking persons of interest”) and when referring to the human body (“A search was made of their persons”), but in one of those curious cases of illogical semantic shift, it has all but disappeared in general usage.
On a related note, some readers are puzzled by peoples, but this is merely the plural form of the collective noun people; “the peoples of the Arctic region,” for example, refers to multiple distinct ethnic groups: the people of here, the people of there, and the people of the other place: the peoples.
People, meanwhile, is occasionally used as a verb synonymous with populate (“We will soon people the entire planet”); the antonym is unpeople. (Populate and people share etymological origin.)