I think “communication skills” should really be thought of as two separate sets of skills.
There are the “hard” communication skills, which are easily visible and which I’m going to call “expository communication skills”. These are things like being articulate, being able to write coherently, being good at public speaking, etc.
Then there are the “soft” communication skills, which I’m going to call “collaboration skills”, which are all about having the ability to understand and influence and compromise and work with other people. These are largely invisible.