First of all, you need to know that the full meaning of FHA is the Federal Housing Administration, while HUD stands for Housing and Urban Development. These two bodies are quite similar in operation, in such that they help individuals to obtain a home, even with low income.
They also help to sell as well as buy homes too. In the United States, FHA is recognized as a part of HUD. The HUD department act became a law in 1965, after which it was established in 1966. The FHA was established in 1934 as a part of the national housing act. However, in the year 1965, the FHA became a part of the HUD.
Another main difference between the HUD and FHA is that the former deals with commercial and multi-family housing loans, while the latter deals with individual buyers. The Federal Housing Administration Loans are known to be more flexible than other HUD's conventional loans, and it is also more sort after.