A precise definition in the abstract would be difficult. However, examples are still very useful. Typically, there's an initial easier screening followed by a much harder coding test. Rather than discuss them in the abstract, why not provide clear examples of each?
For example, consider the difference between the three statements:
You'd be amazed with how many candidates can't actually program. Like at all.
vs.
You'd be amazed with how many supposedly 'senior' programmers can't pass a very simple programming test. And even those who do can't handle relatively elementary data structures and algorithms once they get to the second round.
vs.
You'd be amazed how many supposedly 'senior' programmers can't code up fizz buzz or sum odd numbers from 1 to 100 in a loop. And even the ones who do can't search a binary of integers to see if it contains a particular value at a whiteboard in 45 minutes.
The last one doesn't define what an easy and hard problem is in the abstract universal case, but it gives me a very good sense of who is and isn't failing these tests. Without that, the claim is relatively meaningless.
Unfortunately, I actually think that many of these claims are deliberately left ambiguous. Many people who are claiming a shortage really don't want to be clear about why.
Yes, they never define it, because it's really hard work to clearly define what the bar is in terms of a know coding problem (like fizz-biz).