As nouns the difference between pseudepigrapha and apocrypha

is that pseudepigrapha is writings falsely ascribed to famous persons (historical or mythical) to give texts greater legitimacy. Such compositions -- for example, the Περὶ Κόσμου of Pseudo-Aristotle, De unius in re publica dominatione by Pseudo-Plutarch, the Liber Antiquitatum Biblicarum by Pseudo-Philo, the Liber fornacum of Pseudo-Geber, the Psalms of Solomon by Pseudo-Solomon, etc. -- were usually composed many centuries after the ostensible author had died while apocrypha is something, as a writing, that is of doubtful authorship or authority formerly also used attributively.

As a proper noun Apocrypha is

that group of works which formed part of the Septuagint, but not of the Hebrew canon recognized by the Jews, and which is considered by some Christians to form an authentic part of Scripture, but which is rejected by other (namely by Protestants).