A mortgage broker provides loans to clients using relationships with mortgage bankers or lenders. They usually have many different sources to fund loans.
A mortgage banker funds loans from lines of credit that they have established with banks. They then package and sell their loans on the secondary market.
A mortgage lender is an entity who makes a real estate loan. ie. mortgage banker, a bank, an insurance company, etc...
A broker or banker can lock your rate and have your loan underwritten. A mortgage banker would hold this on their line of credit until they sell it. Then the servicer (the one who receives your payments) holds the loan for the owner of the mortgage back security. The servicer could still be the mortgage banker that provided your mortgage, but it could also be a different servicer.
Sallie Mae is affliated with student loans. I think you might have been referring to Fannie Mae (FNMA) or Freddie Mac (FHLMC), these conforming loans are underwritten to guidelines published by these entities. This allows mortgage bankers to streamline the sale of loans on the secondary market. The problems that have been disucssed in the media about non-conforming loans.
Selling loans on the secondary market allows the lender to lend out there money, many times over instead of once every 30 years.
Here's another twist: Lenders and Banks can act as a mortgage broker. Many banks and lenders originate the loan but do not "service" the loan past the first 2-3 payments. Brokers can not service a loan. And many banks offer their loans through a dedicated mortgage-only subsidiary.
No matter whom you use - Banker, Lender, or Broker - once your loan is signed, it doesn't matter who services the loan or to whom the loan is sold... your terms cannot change.
A mortgage banker operates under most of the same rules as a mortgage lender but they are not required to reveal on the settlement statement the service release premium they are making from the lender.
A mortgage broker is required to reveal their yield spread on the settlement statement.
Regardless of whether you choose to use a banker or a broker, maie certain they are someone you trust.