In some cases, terrify can be replaced by terrorize. One of the meanings of terrorize is to terrify. However, terrorize has another meaning, one that cannot be replaced with terrify. If someone intentionally forces or coerces a victim to do something (or not to do something) , then they have terrorized the victim. That act cannot be replaced with terrify, even though the victim can be said to be terrified by the act. In short, if a person is just frightened or horrified, they have been terrified and terrorized. If they have been coerced by threats or action, they have been terrorized, but not terrified (in the same sense).

Mao terrorized the people. A scary movie terrifies you. You can't use "terrify" in your sentence.