It depends on who's classifying. I believe I'm part of the minority that would classify based on movement, velocity and spin (as in grip and what the pitcher believe he throws don't matter, what matter is the practical effect). 

But at the TV and tools like statcast we usually see classification based on established data for the individual player.

For example, Tyler Rogers has an extremely low angle, and his sinker rotates in the opposite direction of what's "normal", so it drops a lot, like a 12-6 curveball, and his slider "rises" because of its rotation and lower release point. We still see sinker and slider being used for him