To sum up the long discussion in comments:
As you've discovered in your searching, there is no standard naming convention for the amount of unthreaded portion of a screw or bolt. There is probably no standard amount of unthreaded portion between manufacturers, and likely not standard within a single manufacturer when comparing screws to bolts and different styles of bolts.
Unless you're an engineer designing and ordering a very large quantity of bolts that need to meet specific requirements for the assembly of a specific item, you simply buy a screw or bolt that meets your requirement of length, diameter, and pitch (particularly for machine screws or bolts/nuts). If it happens to have an unthreaded portion, it does, if it doesn't, it doesn't.
And, as always, there's an XKCD for everything: