Not sure I totally agree with you (big surprise).
In my world, "whilst" we often cure, rub, or inject, the definition of smoking doesn't depend on treating the meat (or other food product) with anything other than smoke (which is, as you imply, usually applied at a "lower" temperature - say up to about 250)o.
Also, many consider BBQ & smoking as pretty much the same method (both using low, indirect heat), the major difference (if any) being the presence/absence of smoke as a major flavor component.