If someone graduates law school but does NOT take the bar exam...?

Yes. "J.D." refers to the degree. They can even say they are a lawyer, they just aren't admitted to the bar or allowed to practice law.

Its not that uncommon for a lawyer to not take the bar, especially if they are going to work for a major corporation and are only doing in-house work, basically acting as a legal consultant.

Contrary to what some people and some universities will tell you, a JD is not a great selling point for someone who doesn't practice law. Employers will always wonder why you incurred such a large expense to not practice law. The suspicion will be that you couldn't figure out what you wanted to do in life, or worse, that you couldn't pass the bar.

Wikipedia is pretty clear on this.

Not all J.D. degree holders sit for the bar exam, and thus not all J.D. holders are licensed attorneys, unless the jurisdiction permits otherwise.

Correct. Once you graduate law school you have a juris doctorate (JD). Once you pass the bar you're a licensed attorney.

JD is just the name of the degree you get when you graduate law school. (It's not the only one - there's also AB among others).

It's OK if you want to write BA, JD after your name on your stationery. You just can't write Attorney at Law.