Financial Aid at Selective Schools

So when looking into selective schools and their net price calculators (Stanford, Harvard or Duke for example) they all seem to offer different amounts which is to be expected. But when looking into the FAFSA is seems to have a significantly higher parent contribution then what the schools calculate it to be. So I am just wondering if these schools offer more then what the FAFSA says they should pay or the FAFSA is a better calculation of their actual contribution.
I hope this question makes sense and thanks for any feedback!

FAFSA is for federal aid, the Pell grants and SEOG, and to qualify for subsidized loans and work study. Some schools use it to award their own aid, or a state may use it to qualify for certain programs. Most of the selective schools that give a lot of need based aid also require the CSS.

Most selective colleges use the CSS Profile to determine the amount of institutional aid that will be awarded. As @twoinanddone said, Fafsa is for the awarding of federal aid (the second “F” in the abbreviation stands for federal). You need to fill out Fafsa to get a Stafford loan and to see if you are eligible for a Pell grant. Many colleges that offer little institutional aid will also rely on Fafsa to calculate its institutional aid (instead of CSS).