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I was considering 3 kinds of 3d board. There is the cubic-cell one, on
which the Bishop/Unicorn distinction is well established. There is the
board of several hexagonal-cell boards with three Rookwise lines on a hex
board and a fourth at right angles to them, which can also be viewed as
square-cell boards joined on the skew. On this there can be square-board
Bishops which can reach any cell, and the hex piece commonly called a
Bishop, which is of little use as it is bound to a third of a single hex
board! Then there is the form of board used in Mark Thompson's Tetragonal
Chess, which can also be viewed as an assemblage of square-or
hexagonal-cell boards. On such a board both pieces can be used with
workable moves, and it would make sense to call the hex-derived one
something different.
One characteristic of the hex piece is the length of its shortest move,
which is root 3 times the Rook's - exactly the same as a Unicorn on a
cubic board. As the cubic- and hex-board root-3 riders can never occur on
the same kind of board, at least within 3 dimensions, it seemed logical to
confound them.