In the Gallican usage, beginning about the seventh century, the Feast of the Cross was celebrated on May 3, and called “Crouchmas” (for “Cross Mass”) or “Roodmas“. When the Gallican and Roman practices were combined, the September date was assigned to commemorating the rescue of the Cross from the Sassanid Persians, and the May date was kept as the Finding of the Holy Cross or Invention of the True Cross to commemorate the finding. (In this context “invention” (from Latin invenire, “to find”) does not have the modern sense of creating something new.) Pope John XXIII removed this duplication in 1960, so that the Roman Calendar now celebrates the Holy Cross only on September 14.
May 3 is the date given in the Church of England‘s Book of Common Prayer liturgy, but the new Common Worship liturgy, following the Roman Catholic Church’s lead, celebrates Holy Cross Day on September 14.