Count me in with the group who does not fret at all whether the d20 roll that adds the ability modifier snd posdible skill or too proficiency was called a skill check or an ability check.Agreed.
To steal one of Dungeon World's Principles, "Begin and end with the fiction."
Also, as noted above, but I feel it needs repeating... There is no such thing as a "skill check" in D&D 5E.
To me it doesnt matter. The term "skill" has been used across a great many systems to differentiate them from attack scores for ages and they seemed to survive just fine.
It doesnt bring any sense of trouble in our actual play if someone says skill check instead of ability check. We arent that hung up on using the new lexicon for the edition which really pushes " rulings" over "rules."
Pondering whether if one house ruled explicitly for your table that ability checks can be referred to ss skill checks without consequences it would be more accepted on forums by those who at least give lip service to house rules being allowed?
Obviously though, a non-AL game.