I think your trying to simplify something that's not that simple. There are many adjectives required that describe a fastener beyond just screws or bolts. They are all screws. A head bolt is a head bolt. It's usually designed for a certain application with a certain head type, strength, diameter and thread length that usually doesn't fall within typical fasteners standards. I'm guessing what you're calling a bolt, is actually a HHCS(hex head cap screw). If you want to take a deep dive into fasteners get a ASTM standards manual for fasteners and materials.
I'm a machinist, so my language doesn't necessarily fit in. If you look up anything in
Machinery's Handbook, it will refer to 'screw threads.' At the hardware store, you select screws from one bin, and nuts from another. We are working with nouns. Anything with an external thread is a screw, like you said. A screw is a simple machine with a head and a helical thread. Engine heads are not secured by nuts, so I confusingly call them 'screws.' Button-head, socket head cap screw, slotted, carriage bolts, or hex, your choice. When you fasten it with a nut,
then it is a bolt. However, regarding fastener failure, the article I posted was illustrating the failure of the screw, at the minor diameter, not broken nuts. Fastener fault consideration involves both ASTM testing, as well as ANSI standards.
Once you get into 'screwdrivers,' the language gets messy. Likewise, 'turning' is a specific operation performed on a lathe. Turning, facing, boring - outter diameter, perpendicular to axis, or cylindrical, respectively. So, mechanics talk about 'turning' brake rotors or drums, that is correct in the garage, and incorrect in the machine shop. Also, a 'drill-bit,' in the machine shop is simply a 'drill,' which is also in the dictionary.
In American English:
Bolt - noun. A fastener consisting of a threaded pin or rod with a head at one end, designed to be inserted through holes in assembled parts
and secured by a mated nut that is tightened by applying torque.