The difference between persons and people.

"people" is a collective noun, and it is used to refer to a group of people collectively.
These people are a community.

"persons" is the plural form of "person" when you want to refer to a number of people individually.
These persons are part of a community.
Note: The word "people" can also be used as a singular noun and pluralized:
That native people has died out.
The invention was worked on by many peoples from all over the world.
Thus, a list can be made:
Person (A person)
Persons (A group of persons individually)
People (A group of persons as a unit)
OR
People (A specific group of persons)
Peoples (Multiple groups of persons)

The use of the word "persons" nowadays is being shifted towards "People". The word "persons" is seldom heard even though it is often grammatically correct (i.e. Four people died is wrong. Four persons died is correct).
Nobody will punish you for using "people" instead of "persons" in most cases, though.
Persons refers to a group of individual humans. You usually refer to persons with a disability, or persons who are high school graduates
People, on the other hand, is a collective noun that simply refers to a group. So you can have 'people who speak Spanish' as opposed to 'persons with Spanish ancestors'
It's a small difference, but it can be important.
Does that help?
You're supposed to use persons when you referring to the exact number or units of people.
Three persons were hit by the car.
Also, people can be plural - peoples.
The peoples of the world rebelled against their respective governments. (Distinguishing that there are different types of people.)