§1. An apostolic vicariate or apostolic prefecture is a certain portion of the people of God which has not yet been established as a diocese due to special circumstances and which, to be shepherded, is entrusted to an apostolic vicar or apostolic prefect who governs it in the name of the Supreme Pontiff.
§2. An apostolic administration is a certain portion of the people of God which is not erected as a diocese by the Supreme Pontiff due to special and particularly grave reasons and whose pastoral care is entrusted to an apostolic administrator who governs it in the name of the Supreme Pontiff.
Source: Code of Canon Law (Vatican.va)