What is the difference between these two structures? Both seem to be quasi-dioceses established in places not yet ready for a proper diocese. Both are typically led by bishops (unlike apostolic prefectures). It is that apostolic vicariates are established in mission countries (having been promoted from “prefecture” or “mission sui iuris” status) while territorial prelatures are established in countries that otherwise have established dioceses?
It seems you have the right idea. I don’t have a lot to add.
You are correct in your last statement: that is one distinction. The territorial prelature is established in places not under the Congregation for evangelization of peoples. However, they are like the vicariates in that they are of a provisional nature and are erected in places that are not able to function as a diocese. On the hierarchy of stability and autonomy, the territorial prelature is below the diocese but above the vicariates.
Another practical distinction is that the vicars who are in charge of the vicariates are, as the name makes clear, vicars. They act in the name of the Pope and so do not have “proper” authority (meaning, they do not exercise authority in their own name).
The Code of Canon Law, if you do not know, mentions these structures in canons 370-371.
Are Territorial Prelates appointed via the Congregation for Bishops as Diocesan Ordinaries are, then? While Apostolic Vicars are appointed via the Congregation for the Evangelization of Peoples…
Yes. See Pastor bonus, articles 75-77 (Cong. for Bishops’ responsibilities) and 89 (Cong. for Ev. of Peoples’ area of competence).