When is a staircase not a staircase?

I have recently been reading  about the history of Hampton Court and came across this footnote that defines “Staircase.”  This is taken from The History of Hampton Court Palace, Volume 3 which was originally published in 1891.

The terms, “stairs,” “staircase,” “pair of stairs,” “Balusters,” etc., are much confused in common parlance.

A “staircase” is properly only the “case,” room or space, that contains the stairs. A “stair” is merely a flight of steps. The term “pair of stairs” has given rise to some discussion, but its obvious explanation is exemplified in nearly every old staircase at Hampton Court. To mount from one storey to another it is necessary  in order that each stair may not be too steep, and to economize on space, that two flights of steps should be used, going in reverse directions. To go from one floor to another therefore, we have to go up “a pair of stairs. ” The level space, or landing, as it is sometimes called, between one pair of stairs and another, is always designated in old writers a “hall-pace,” corrupted into “half-pace.”

To talk, therefore, of a marble staircase, unless the walls are marble is incorrect; as it is also to use the terms, “on the staircase,” “going up the staircase.”