Double Play or Dual Play?

I'm not exactly sure if the term is "Dual Play" or "Double Play", but the menu option in Raiden III (and most likely in Raiden IV) call it Double Play, but I refer to it as either.
Anyway, Dual Play Shooting will be a side topic for me to document my thoughts and experience playing vertical shooting arcade games (also known as shmups) while controlling both player 1 and player 2 ships at the same time. Even though this technique of playing has been around for over 15 years (since the original Raiden days), it was made much more public/popular by VTF-INO with his Ikaruga replays (see youtube example below).