Exploring the nuances: are you "lucky" or "fortunate"?

What is similar?
Both "lucky" and "fortunate" describe a situation or condition where someone experiences good outcomes or favorable situations often without explicit effort or expectation.
What is different?
"Lucky" often implies a more random or chance-based positive outcome, while "fortunate" can suggest a broader or more stable state of having good fortune or being well-off. "Fortunate" can feel slightly more formal than "lucky".
Which one is more common?

Examples of usage
Lucky- She was lucky to find her keys under the couch.
- He's always been lucky with weather on his vacations.
- You were lucky to have caught the last train home.
- They were fortunate to have avoided the storm.
- She feels fortunate to have such supportive friends.
- We are fortunate to have good health care.