"Intimidating" vs. "scary": exploring the language of fear

What is similar?
Both "intimidating" and "scary" describe things that can cause fear or apprehension. They often refer to situations, people, or objects that provoke a sense of fearfulness or unease.
What is different?
"Intimidating" often implies causing feelings of inferiority or awe, particularly through power, size, or confidence, rather than pure fear. "Scary" typically refers to causing fright or fear, often more directly associated with fear-inducing situations or things.
Which one is more common?

Examples of usage
Intimidating- The professor's vast knowledge and stern demeanor made him quite intimidating to the new students.
- Facing the tall, ominous building alone at night felt intimidating to her.
- Negotiating with the formidable CEO was an intimidating experience for the young entrepreneur.
- The horror movie was so scary that I couldn't sleep that night.
- The haunted house gave us a truly scary experience.
- It was scary how quickly the storm approached.