or does the use of the word cancer mean they can only be classified as malignant?

What are some examples?

The other post is correct on terminology. And you also asked for an example of a benign brain tumor.

Pituitary Adenoma.
This is almost always a benign tumor on the pituitary gland, and it's very treatable. Usually with medication and/or surgery. It doesn't require chemo, and almost never spreads to other parts of the body.

cancer is only malignant. benign tumor is one that is not cancer.
Certain TUMORS of the brain can be benign.
Hope it helps.
Good luck!