I’m not sure if the wire gauge thing is right, unless you’re talking about a different system than I’m familiar with, because with wire gauge smaller number=bigger wire, and with screw sizes smaller number=smaller screw

Also just my 2¢ on “machine screw” vs “bolt” as a casual tinkerer with various things held together by different types of threaded fasteners.

Generally speaking if it’s got a hex head or nut that I’m using a wrench to tighten, it’s a bolt

If it’s got some sort of hole (or God forbid a slot) that I’m going to use some sort of a driver (for the purposes of this, an Allen “wrench” is a driver) to tighten, it’s a screw.

And of course everything gets really murky when we start talking about things like sheet metal screws, lag bolts/screws, masonry screws, etc.