FAFSA is used to determine need relative to federal benefits: Pell Grants, guaranteed student loans, and such.
CSS Profile does not calculate and EFC, it is used to gather all the information that the school will plug into their own formula. Thus your son will have a different “need” at each of the schools using the Profile. There will even be questions on the CSS Profile that only apply to some schools, and not others (if you don’t select schools requiring certain information, you won’t be asked for it).
Thus, you third statement is mostly accurate - with CSS Profile, the school is determining how to distribute their own money, so they prefer more data. More data generally means more accuracy for their needs. FAFSA will still be used to qualify for any appropriate federal aid, as a Pell Grant would be government funded, and would reduce the amount of institutional aid necessary to meet your need.