The singular noun regarding homo sapiens is "person". The plural, is usually "people". Though, some instructions of legal sounding verbiage use "persons". What then is the difference?
I would suggest, that "people" being singular, refers to many acting as one. As such, Americans are a people, and not a gaggle of persons. Take two such large groups, and we have "peoples". Again, not persons.
Person, therefore, refers to an individual entity that cares not for groups. As such, two individuals referred to in the same sentence would be persons. The lottery awarded prizes to two persons, not two people. Though, they are the people that won the award, not the persons that won the award.
This would explain why people use "people". Why divide if we don't have to? Though, legal jargon usually deals with individuals, so it uses persons.
Hmm... i'm not sure if that even makes any sense.
(On a side note, i originally spelled "grammar" as "grammer". Now that's funny.