Should be the same name - draw bar. Principle of clamping is very similar. Pullstud is "hooked" from outside in case of CAT and ISO toolholders. In case of HSK toolholder internal clamp is used.
Action of drawbar is pretty the same - the spring pulls drawbar back ( up ) with about 9 tons force clamping the tool. Activated hydraulics pushes the draw bar forward ( down ) releasing the toolholder.
Design of HSK