'parts of "East Jerusalem" for example are to the south and west, as in Gilo.' This all presupposes that anyone recognises the new city boundary that Israel imposed in 1967. The problem is that no one does. An occupying army can not legitimately meddle in civil affairs or annex land, both are prohibited in international law. So Gilo, Giv'at HaMatos and Har Homa legally remain in Bethlehem Governorate, illegal settlements on illegally-annexed land. Just like Ramot Allon, Pisgat Z'ev, French Hill etc are illegal settlements in Ramallah Governorate. The term 'East Jerusalem', which pre-1967 referred specifically to the Arab municipality of E J'sem, is today used generically - by the USA (Baker), UN, EU, international courts etc - to describe ALL the land surrounding Jerusalem which Israel illegally appropriated.
from the article: EU envoys: Israel trying to sever East Jerusalem from West Bank