Is a realtor and real-estate agent the same thing?

No, a real estate agent has a license to sell under a broker. A realtor does as well, but in addition they belong to NAR, the National Association of Realtors. The word is actually trademarked and can not be used by a non-member.
...............................................................................
Dog Ma (and others) hit the nail on the head.

People use the terms interchangeably but they aren't really the same thing.

A real estate agent is any one with an agent's license to work for a broker in the real estate business.

A Realtor is a member of the real estate association. It's a trademarked name, not that it's made any difference in vernacular usage.

Realtor's have to meet certain guidelines of behavior and continuing education that an agent may not.

All Realtors are either agents or brokers, but not all agents are Realtors.
...............................................................................
Although I'm not in the business, I'd say the "agent" word is a more definitive status of not being a "broker", who commands having multiple agents working for them. The realtor word is likely used for either but be sure to understand that a broker is likely more experienced having others working for them.
...............................................................................
Not in Canada. A real estate agent is someone who sells real estate. All they need is a license. A realtor is a real estate agent who belongs to a professional association and has earned (through additional training) the realtor designation and must adhere to a code of ethics.
...............................................................................
A Realtor is a member of the National Association of Realtors and is entitled to use the term. Almost all US real estate agents are Realtors, but I would not recommend using one that is not.
...............................................................................
by definition, a real estate agent sells realty, while a realtor sells AND buys realty. the testing & licensing requirements are not the same.
...............................................................................
generally yes, although a realtor could also be a real estate broker
...............................................................................
Yes.
...............................................................................
Yup.
...............................................................................
yes