ACF accreditation only applies to cooking programs. ACCSCT is a more general accreditation organisation which oversees non-four year vocational programs. All community colleges are state and nationally accredited by the Accrediting Commision for Community and Junior Colleges. Elgin College in Illinois, for example, has a culinary program accredited by the ACF AND the Accrediting Commision.
Private vocational institutions may be accredited by different commisions but may fail to meet national standards for general education requirements. As a result, many JC's and 4-year schools don't accept credits from private 2-year schools. The ideal combination, in my opinion, is to go to an ACF accredited program at a JC for the following reasons:
1) You get a broader education which includes music, art, humanities, and physical sciences.
2) In the event that you feel you're not the next Charlie Trotter, you can change programs and become a physicist.
3) Variety of classes like golf, Science Fiction, and ceramics.
4) If you decide to get a business degree you can transfer to a 4-year school.
5) Affordable tuition, used books, student life, sports!