Note: This post is NOT a duplicate of "is more commonly used" vs. "more common", which is focusing on the difference between "be more commonly used" and "be more common".
This post focuses on the difference between "is commonly used" and "sounds natural/is idiomatic".
As you may have noticed, I treated "sounds natural" and "is idiomatic" as the same. There are 3 pieces of consideration.
A nice answerer's opinion
First of all, non-native English speakers alway care about whether what they say sounds natural. So, lots of people ask whether some expressions are idiomatic. I also ask this kind of question a lot, such as Is it idiomatic to say "could only be used"? and the following.
An answer to the post Is it idiomatic to say "grammatical and idiomatic"? says
... it is both grammatical and idiomatic in the sense that it sounds natural, but it is not really what you could call a "commonly used" phrase.
which conveys, I suppose, that some expressions sounds natural are usually idiomatic.
I put a group of phrases on Google Ngram and got this.
Which illustrates clearly that "sounds natural" and "is idiomatic" have almost the same points.
Cambridge Dictionary gives this definition about "idiomatic"
containing expressions that are natural and correct
Obviously, idiomatic and natural are synonyms each other.
The last and the most difficult part is the difference between "is commonly used" and "sounds natural/is idiomatic".
The part that I quoted earlier also implies that, some expressions sounds natural are not really "commonly used". For example, "grammatical and idiomatic" might sounds natural but it is not really "commonly used".
The Google Ngram also suggests that "commonly used" is really commonly used than "sounds natural/is idiomatic".
Why is that? Could someone explain a bit more? Could someone name more examples where some expression sounds natural are not "commonly used"?