Most of the other answers from licensees describe the difference between an agent and a broker. Imagine their surprise when I say what I’m about to say: in my state, ALL real estate licensees are brokers!
The number one rule about real estate law and practice in the US is that it varies widely from one state to another. I prefer to answer questions as they pertain to local law and practice since in other jurisdictions, those answers may or may not be accurate.
Brokers are generally responsible for more legal compliance and are required to face additional training. In my state, we all operate at a higher than expected level because we have the training and licensure to do so.