I think the line is one of how much the bottom/sub/slave lets their lover choose what's going on.

A bottom is allowing their choices to be made by their partner, and then choosing to stay passive (go along with them) or to let their lover know it's not good for them.
A sub is giving their choices to their partner, even if the choices aren't ones they particularly like, and going with it (to the degree they're comfortable with).
A slave is relinquishing their choices, and accepting a punishment if they don't go along with the descisions made.