I would question the distinctions significance in the context of my original post, to be honest.
And I would not categorise Leonard Cohen as pop music, by your criterion, as it would not be useful. "Pop music" as a term used by the music industry changes it's definition along with people's musical taste. If you take the right moment in time, an extremely broad variety of music would be "pop music".
"popular music" != "pop music"
The term "popular music" is an umbrella for music that has "wide appeal" and associated with "large audiences" [0] -- i.e. it's a statistical term.
It can apply to many "genres" (that's the music industry term, rather than categories).
One of those genres[1] is "pop music"[2]. And after your clarification, I now assume your OP actually meant "pop music".
[0] https://en.wikipedia.org/wiki/Popular_music [1] https://en.wikipedia.org/wiki/Music_genre [2] https://en.wikipedia.org/wiki/Pop_music