You could split it a dozen different ways, and every one would be wrong. According to someone, anyway.
IRL I'm solidly built, with broad shoulders. Heavy upper body (I look a lot stronger than I am.) I used to be a professional magician. Agile, I'm not. I used to be able to walk a tightrope and ride a unicycle, but that was forty years ago.
My manual dexterity is off-the-chart for most people.
I can't hit a basket in basketball and never could. So my hand-eye coordination sucks.
So what part of that odd mix is Ability Score and what part is practiced skill? To make an item "pop" into existence in my fingers, I have to bring it from a hidden location to final view in less than 1/15th of a second. At that speed the human eye can't register the motion (medical fact involving the synapses in the optic nerve.). The coin, or whatever, is "just there" - Poof. Magic. While the skill is required, most people simply don't have the nerve and/or muscle speed to pull that off, so that's Ability Score.
Even as a kid I couldn't hit a trash can with a piece of paper. With practice I can throw a playing card and hit a small target across the room, but that doesn't translate to accuracy with anything else. I'm a decent shot with a bow, and have a few minor archery tournament prizes to my name. So my hand/eye disability is "Ability score", and my archery and playing-card accuracy are simply enough skill training to overcome the bad score.
Similarly, tightrope and unicycle are trained skills, not evidence of an exceptional ability score. I'm not clumsy on my feet, but I'm not anything exceptional either.