The words persons and people are the plural forms of the noun person. They are not used in exactly the same way.
People is by far the more common of these two expressions and is mainly used in ordinary writing.
- Some people were waiting outside.
- Will people ever live 200 years?
The word persons is mainly used in official or formal writing.
- This car can seat 7 persons.
Note that the plural form peoples is sometimes used to refer to the members of a particular nation or community.
In strict usage, the word people is used to refer to an indefinite number of individuals. The word persons, on the other hand, is used where a precise number is specified.
- The auditorium can seat hundreds of people. (indefinite number)
- This hall can only seat 50 persons. (definite number)