Softening the impact: "downplay" vs. "understate"

What is similar?
Both "downplay" and "understate" involve presenting something as less important or severe than it actually is.
What is different?
"Downplay" often implies an intentional effort to minimize or dismiss the significance of something, possibly to mislead or deflect attention. "Understate" typically refers to expressing something in a restrained or modest manner, without necessarily intending to deceive.
Which one is more common?

Examples of usage
Downplay- The company tried to downplay the impact of the data breach.
- He downplayed his injury to stay in the game.
- Officials attempted to downplay the severity of the approaching storm.
- She tends to understate her achievements.
- The initial estimates understated the project's true cost.
- His humble speech understated the significance of his discovery.