The first answer explains Broker/ Agent well, the agent works under a Broker for a period of time (depending on state) before they can become a broker, butthey do not have to become a broker. The benifit of being a broker is that you get a cut of the commission earned by agents you supervise (varies by office), they get this because they usualy carry the Errors and ommissions insurance that covers them and their agents and have experiance and time invested but this also involves a higher risk.
Real Estate agents list property for sellers for an agreed commission to be paid at closing on an accepted offer. They earn this $ because they will advertize the property prepare paperwork work with the lenders, show the property,work with the title companies and take on liability durring the transaction. For buyers a Realtor is like a search engine who will alert a buyer to potential properties and help them with their offer and through the transaction of buying a property (they are generaly paid from the commission paid by the seller) They only get paid in this instance if the buyer actually buys a property. this is why they will generaly require proof of financing before they will even give you the time of day. All in all the job is Great fun, hard work.

An Agent hangs their license with a broker who is ultimately responsible for all agents under him/her.
Broker must be an agent for a minimum of 4 years and pass the state exam.