Yes, gamepad == joystick == controller. Since I haven’t tested every controller out there, I’m sure there’s some exceptions but they do a great job trying to keep things uniform. The buttons are referred to by their physical location, if you go to the Input Map and expand the Joystick Buttons section, Button 0 is the “Bottom Action = Sony Cross, Xbox A, Nintendo B” so it doesn’t matter which controller type you have, it’s the bottom button. And at this point in time, most 3rd party controllers are for those systems so register correctly.
Even if you don’t have a gamepad, if you’re just using keyboard I recommend adding the gamepad actions since it’s so easy (and you can note on the your page that gamepad is there but untested if you’re nervous about it).