Metochia/Metochion being dependencies of a monastery (ie, other monasteries, hermitages, parishes, missions, etc.) The Slavic word is Podvorje - similar to how in the West (specifically Ireland and Britain) the word paruchia (paruchiae - ie, the Columban paruchia, the Patrician paruchia, the Culdee paruchia, etc.) developed from the original Latin term parochia (meaning parish) to a term describing a mother monastic institution and its daughter dependencies: monastic, clerical and lay. I think Brotherhoods are also similar.
(I don't really know about Met. Paisios - just noticed that they use that system of metochia as a stavrophegial monastery, and that they are Greek. Not sure some would appreciate it being spoken of in private, but private emails are welcome on sensitive matters.)