"Widen" vs. "extend": exploring their unique dimensions

What is similar?
Both "widen" and "extend" refer to increasing dimensions or scope. They can both be used to describe physical changes or metaphorical expansions.
What is different?
"Widen" specifically refers to making something broader or wider, typically related to width. "Extend" is more general and can refer to increasing length, time, or scope, not limited to width.
Which one is more common?

Examples of usage
Widen- They plan to widen the road to allow for more traffic.
- She wants to widen her vocabulary by learning new words.
- The river begins to widen as it approaches the sea.
- They decided to extend the deadline by a week.
- The company plans to extend its services to other countries.
- He extended his hand in greeting.