I think the adjective would depend on the posting. Hence, we have foreign correspondents. Spy networks have our man in [Hong Kong, Portugal etc]. Baseball teams have their South American [or other designated overseas territories] scouts.
BE usage is, errr... special. In the U.S. overseas and abroad obviously do not overlap with the same frequency that they do in the U.K. For a Mexican citizen, the U.S. and Belize are abroad, but certainly not overseas. Liliput has made the point pointedly.