A word to describe vertical and horizontal movement?

Imagine the 'Bishop' chess piece. The four directions that it can move can be called 'diagonal'.

Similarly the 'Castle' moves in the horizontal and vertical directions. Is there a single word that describes this movement?

The rook in chess moves orthogonally.

This term is not used often (unlike diagonally) as more authors seem to prefer to spell things out (i.e., horizontally and vertically) to prevent being misunderstood. Still, it can be traced in many chess manuals, such as this one (cf. Basic play section, p. 2).

Orthogonal literally means "along angles", while diagonal means "across angles", where the word angle needs to be understood as "the right angle".