"Distortion" is a lens defect and in images like those, when uncorrected, would show very clearly and would disturb the subject a lot.
Distorted means deformed, wrong, weird, not-straight. Geometric and perspective effects should be rendered with some other word than "distortion" because they are perfectly normal real-world phenomena and show nothing "deformed".
I understand that people use the term geometric or perspective "distortion" when talking about the exaggerated nose of somebody photographed with a wide-angle lens from short distance.
But in general how do we define "barrel-pincushion/moustache distortion"? Should we define each time "of the barrel-pincushion kind" to be clear?