Some apparently commonly held notions of the defining characteristics of bolts vs screws are incorrect and inherently ambiguous. One consequence of some confused definitions is that a bolt would suddenly be transformed into a "screw" as soon as its nut is removed. That would be arbitrary and inaccurate. The proper distinction is simply that a bolt is a headed externally threaded fastener that has a standard bolt thread (there are many different standards), and can therefore accept a nut (of the appropriate bolt-thread standard). If the nut is removed from the bolt, the bolt is of course still a bolt. A bolt does not need a nut for it to be a bolt. This means that a cylinder-head bolt is a bolt because it has a bolt thread, and could in principle accept a nut. A screw on the other hand does not have a standard bolt thread, and therefore does not accept a nut. An additional qualifier is that bolts are not tapered, but screws may or may not be tapered.
The proper definition
makes no assumptions
about size, head style, shank length or application, it simply defines the objects in question.