"Cooperate" vs. "collaborate": twin pillars of teamwork explored

What is similar?
Both "cooperate" and "collaborate" involve working with others towards a common goal or task. They both imply a level of partnership or teamwork.
What is different?
To "cooperate" often means to act together or in compliance without necessarily achieving something new as a unified effort. It can imply more basic or routine assistance. To "collaborate" typically suggests a deeper joint effort where all parties actively contribute to achieving a specific goal or creative outcome.
Which one is more common?

Examples of usage
Cooperate- The two companies agreed to cooperate on the new project.
- To solve the problem, we must all cooperate and share our resources.
- Scientists from around the world collaborated on the research paper.
- The artists decided to collaborate on a new piece for the exhibition.