The purpose of
Affidavit of Support Form(a promise to support), is used to show USCIS that a the permanent residence or US Citizen for the Alien to enter US. He/she must show sufficient financial resources to provide for the alien, and should prove she won't become a public charge.
There is no fee for
Form I-134, to be used for aliens seeking admission or adjustment of permanent residence as immediate relatives, family-based immigrants, and certain employed-based immigrants.