The Federal Housing Administration (FHA) was an outcome of the National Housing Act of 1934 and been a part of the U.S. Department of Housing and Urban Development since 1965. It was created to help make homeownership more affordable to Americans after coming out of the great depression.
A conventional mortgage is a home loan that is NOT backed by a government agency like FHA or VA. They often meet the down payment and income requirements set by Fannie Mae & Freddie Mac. They have stricter guidelines to qualify than compared to government-issued loans.
A VA stands for the Veterans Administration. It is a mortgage loan that is guaranteed by the United States of Veterans Affairs. This loan program is the preferred loan program for active, non-active, national guard, reserve and retired military of the armed forces. This loan program requires no down payment and no private monthly mortgage insurance.
A USDA loan stands for the United States Department of Agriculture. They have backing from the U.S. Department of Agriculture as part of its USDA Rural Development Guaranteed Housing Loan Program. They are available to home buyers with low-to-average income for the area in which they live.