For practical purposes, people is basically always right. Except for those few times when persons is right…
I mentioned before how the word people is understandably confusing for English learners, who will often use persons. One thing I didn’t mention back then though was the fact that, as you’re no doubt aware, sometimes persons is correct.
If you’re a native speaker, you’ve probably never used it in conversation, but there’s a good chance that you’ve seen it written on a sign somewhere. In a lift maybe, saying something like Maximum Occupancy: 12 persons. If you think about why someone might use persons instead of people in a case like this, the reason’s pretty clear and simple. You don’t want there to be any doubt as to how many people can safely occupy your lift, and considering how people can be confusing for non-native speakers, it’s safer to go with persons, which is clear to everyone.
A little bit like how stop signs around the world are in English. It’s a pleasant and rare enough case of the English-speaking world being briefly aware that some aspects of the language can be confusing, and acting accordingly. Not that that’s the only reason for using persons though.
You might also have noticed it used in very formal contexts, often in legal documents. The main reason for this is that precision is so important in legal language, and no-one is going to be confused by refererences to three persons, for example. It also makes it easier to write person(s) than a person or people. Legally though, there is a distinction between persons and people, in most parts of the world. Because you see a person, legally, is not always a person.
Many legal jurisdictions have the concept of a legal person, which most of the time is a person, like you or me, but can also be extended to other entitites. A legal person is usually recognised as any entity that is recognised as having certain privileges, such as having the ability to enter contracts, or to sue and be sued. In addition to actual people, this definition can also be applied to states, counties, corporations, or other entities comprised of multiple people.
Legally therefore, people simply refers to multiple people, but persons refers specifically to individuals or entities recognised as legal persons.
But yes, generally people is fine!