Indeed, but my understanding is that it was called "The West" (Algarve) because it is at the western part of the Iberian peninsula, and considering from the viewpoint of one who lives in the south anyway it makes more sense. Here is a web page with a simple map, also showing VilaMoura:
http://www.algarve-web.com/algarve/index.htm
I have enjoyed this communication, took me to my younger days (when I argued anything that is ).