Twin-stick shooter

The emphasis here is that no button is needed to be pressed to shoot, only to twist the (joy)stick in direction you want to do so. Exception being that the player has buttons separately for each direction and are independent of movement.

This is NOT synonym for shooters which use dual-analog controllers.

This can also apply to games without any stick controlllers, such as each attack/shooting direction (not different attack) has separate button (e.g. numpad).

Implied: independent aiming (at least if it's top-down perspective), dual analog gamepad