FHA: The Federal Housing Administration (FHA), which is part of the U.S. Dept. of Housing and Urban Development (HUD), administers various mortgage loan programs. The FHA can help people to obtain a loan with little or no down payment. The FHA does not supply the loan; it simply insures the loan to limit the risk to the lender.
The FHA loan guidelines are more relaxed than conventional loan guidelines; this includes less strict regulations about job requirements, use of alternative credit, and debt to income ratios.
VA: VA loans are guaranteed by the U.S. Dept. of Veterans Affairs. The guaranty allows veterans and service persons to obtain home loans with favorable terms, usually without a down payment. The U.S. Department of Veterans Affairs does not make loans, it guarantees loans made by lenders. VA determines your eligibility and, if you are qualified, VA will issue you a certificate of eligibility to be used in applying for a VA loan.