People is the plural form of person. It can talk about a group of individuals or a whole national, racial or ethnic group.
Peoples is very formal and is only used in academic literature. It only talks about a whole national, racial or ethnic group.
Persons is formal and bureaucratic and is only used on public notices in such places as lifts, parks, buses, and in legal documents.
I invited 15 persons to the meeting, but only five came.
I invited 15 people to the meeting, but only five came.- The people of western Europe generally enjoy a high standard of living.
- Similar customs and traditions are to be found among many peoples of the world.
- MAXIMUM 15 PERSONS IN THIS LIFT
The word persons in general use is wrong. The correct word is people. You will almost certainly never need to use the words peoples and persons.
