The “cross of Jerusalem” is taken from the arms of that Kingdom. The Kingdom of Jerusalem had a variety of crosses through its life; this is the best known form, dating from 1282 [ANA2 339]. Period blazons didn’t use the term, instead explicitly blazoning it by parts, e.g., “a cross potent between four crosses couped.”
Stephan of Monmouth bears: Per pale Or and sable, a cross of Jerusalem counterchanged.
Lothar Hügelman bears: Sable, a cross of Jerusalem argent.
Lucien de Wyntere bears: Azure, a cross of Jerusalem within a bordure argent.