Yes, I suppose my definition of "outward" would include continuing in the same direction, so what you say does apply to Cannons with he folowing two caveats:
(1) The Korean Cannon can also make an orthognal Grasshopper move without a Rook move following it, whereas the Mao cannot make a Wazir step without then making a Ferz step and so its octagonal analogue cannot make a Wazir or Ferz step without then making a Knight leap. Another way to look at the Korean Cannon is that it makes an orthogonal Cntragrasshopper move preceded by an optional Rook move.
(2) The Chinese Cannon is something more complicated, a divergent piece that can make a noncapturing move only as a Rook but a capturing one only as a Korean Cannon.
(1) The Korean Cannon can also make an orthognal Grasshopper move without a Rook move following it, whereas the Mao cannot make a Wazir step without then making a Ferz step and so its octagonal analogue cannot make a Wazir or Ferz step without then making a Knight leap. Another way to look at the Korean Cannon is that it makes an orthogonal Cntragrasshopper move preceded by an optional Rook move.
(2) The Chinese Cannon is something more complicated, a divergent piece that can make a noncapturing move only as a Rook but a capturing one only as a Korean Cannon.