Both of these terms refer to elements of tradedy according to Aristotle.
Anagnorisis occurs first. It is a character's realization of his or someone else's real identity or character. For example, this occurs when Oedipus learns that he unwittingly murdered his father and married his mother.
Aristotle felt that paripeteia arises from anagnorisis. Paripeteia (peripety in English) is a reversal of circumstances, or a turning point. So, for example, as a result of the anagnorisis, Oedipus' mother commits suicide and Oedipus blinds himself and goes into exile.