Typically these private lenders require more documentation and have more requirements for the borrower, however they are more forgiving than conventional lenders.
FHA has to operate within a different set of rules than conventional lenders (for example they are not allowed to reduce the principal balance of mortgages because it's prohibited by law).
FHA offers higher loan - to - value refinance terms than conventional lenders, and may also help with rolling home equity loans into a new mortgage loan.