You implied that the reason one cannot hang drywall with machine bolts is specifically because they're
bolts. If being called bolts vs screws were such a reliable indicator of functionality, then one would expect sheet metal screws to be much better at hanging drywall than say flat head machine bolts.
BTW I personally call them machine screws. To me, the difference has more to do with what kind of drive they take, whether they're self-tapping, how big they are, or really just what kind of mood one is in.
I'm well aware of many types of threaded fasteners, which is what makes trying for a general formal distinction between bolts and screws seem ridiculous. To me, it seems like more a matter of personal taste and dialect, bureaucrats attempting to force their prescriptions onto the world notwithstanding.
Any one definition can capture most of the distinction, but leaves a remainder that's outright wrong. The CBP definition seems intuitively decent until you realize that the same item will be a screw or a bolt depending on the intent of the user. That's exactly the kind of ambiguity that keeps lawyers entrenched and erodes the rule of law.
If a welded nut breaks free, does its screw become a bolt? When a nut gets tight enough to not spin on its own, does a bolt change into a screw?