A lender is a financial institution that lends directly to you. A broker doesn't lend money. A broker can work with many lenders. Your mortgage lender is the financial institution that lent you the money.
Your mortgage servicer is the company that sends you your mortgage statements. Your servicing entity also handles the day-to-day administration tasks of your loan. Non-bank lenders are not considered to be large scale banks because they do not offer lending or deposit services.