"Cheerful" vs. "happy": discover the nuances of joy

What is similar?
Both words describe positive emotional states and are often used to express joy or contentment.
What is different?
Cheerful often implies a visible, outward expression of happiness and a tendency to be optimistic, often in a manner that is consistent and character-based. Happy is a more general term that refers to a state of contentment, pleasure, or satisfaction and can be either transient or enduring.
Which one is more common?

Examples of usage
Cheerful- She always has a cheerful attitude, even on rainy days.
- The cheerful decorations brightened up the room.
- His cheerful demeanor makes working with him enjoyable.
- She was happy to receive the good news.
- The happy child laughed as he played in the park.
- They were happy with the results of the project.