FHA Loans are insured by the Federal Housing Administration. That means that lenders are more likely to approve a loan with a smaller down-payment.
Conventional Loans are mortgage loans that are not insured by the government (like FHA, VA, USDA Loans), but they typically meet the lending guidelines that have been set by Fannie Mae or Freddie Mac.
Are you a first-time home buyer? Will you occupy the residence that you are looking to purchase? Then a CAlHFA loan may be just right for you.