"Cancel correctness" makes a lot of sense, because it puts the cancellation in some context.

I don't like the "cancel safety" term. Not only it's unrelated to the Rust's concept of safety, it's also unnecessarily judgemental.

Safe/unsafe implies there's a better or worse behavior, but what is desirable for cancellation to do is highly context-dependent.

Futures awaiting spawned tasks are called "cancellation safe", because they won't stop the task when dropped. But that's not an inherently safe behavior – leaving tasks running after their spawner has been cancelled could be a bug: piling up work that won't be used, and even interfering with the rest of the program by keeping locks locked or ports used. OTOH a spawn handle that stops the task when dropped would be called "cancellation unsafe", despite being a very useful construct specifically for propagating cleanup to dependent tasks.