This lack of differentiation really grinds my gears. Why in the world do both of these activities share a name? It would be really interesting to take a random sample of the population and ask them some basic context like their occupation/education, and ask them whether a digital signature comprises a graphic of handwriting (validated with eyeballs) or something more sophisticated (validated with math).
There will be some obvious trends, but I suspect there will also be some surprises.