Is there a difference between Tibet and the Tibet Autonomous Region?

Yes, there is a major difference in these two terms.

The term "Tibet" refers to the entire Tibetan Plateau where the Tibetan people are native to.

The Tibet Autonomous Region (TAR) refers to only 50% of the land mass of the Tibetan Plateau. Parts of Tibet are spread across 5 provinces and regions of southwestern China. Don't let the lines of a Chinese map confuse you. Tibet is a much, much larger area than just the TAR. Roughly 60% of the Tibetan people live outside of the TAR in other regions of Tibet. The terms 'Tibet' and 'Tibet Autonomous Region' mean two very different things.