As a quick rule of thumb would be to never trust anyone who claims "regression" is a separate topic from "classification". Oh yes, and in this case it is beyond awful.
This is what the comment means when it says the division between regression and classification is often artificial (i.e., imposed by people who are concentrating on taxonomy).
Regression is often used to mean regression with infinite range, but especially since so many classification techniques are just searching for a regular partition of an infinite range, the distinction isn't made much anymore. Whether the rare techniques that are specifically over a discrete finite range still count as regression depends on who you ask - usually yes.
While every method I can think of differentiates itself at a lower level than regression/classification, and thus has interpretations in each, it's not always feasible or easy to make the "flip". Often times the approximation steps that make the algorithm tractable depend on the objective function.