What is the difference between a
Realtor and a real estate agent?
The difference is significant. First off, let me say that all Realtors are real estate agents, but not all real estate agents are Realtors.

Realtors are due paying members of the National Assoociation of Realtors, and their respective State and Local Associations. They are usually more trained and educated, and hold designations that demonstrates this higher level of training and expertise. Non-realtors can not hold designations.
Realtors are bound to a Code of Ethics and a Professional Standards of Practice which monitors, governs and enforces the behavior and practices of Realtors, much like doctors and lawyers. So you can be assured that when you work with a Realtor you are working with someone with integrity and a commitment to their profession.
While there are good and not so good in every profession, it is comforting to know that if you are not treated properly and correctly by your Realtor, you do have courses of action at your disposable that would not be otherwise available working with someone who is not a Realtor. Look for the Realtor logo or the designations that follow their names.