The Full Kaddish is recited after the Shemone Esray. It includes a request that the Shemone Esray just recited should be accepted by G-d. It should be recited by the same person that led the Shemone Esray. For example, on mornings that Hallel is recited, if a different person recites Hallel than the person who recited the Shemone Esray, then the person that recited Shemone Esray would say the Full Kaddish after Hallel.