It's not unusual to call control sticks joysticks (as seen here in the definition of analog stick)
But it is a little less usual to call the whole controller a joystick
But it is a little less usual to call the whole controller a joystick
A joystick is more like the one to control airplanes.
I know the gamepad can have sticks but they are no «joysticks» only sticks.
Please correct me if I am wrong.