Wikipedia
The Norse-Gaels (, ) were a people who dominated much of the Irish Sea region, including the Isle of Man, western Scotland and eastern Ireland for a part of the Middle Ages; they were of Gaelic and North Germanic origin and as a whole exhibited a great deal of Gaelic and Norse cultural syncretism. Other modern terms used include Hiberno-Norse and foreign Gaels.
The correct translation for Gall-Ghàidheil or any of the variant spellings is "Foreign Gaels" and although it can in theory mean any Gael of foreign aspect or origin, it was in practice always used of Gaels (i.e. Gaelic-speakers) with some kind of Norse identity. This term is subject to a large range of variations depending on chronological and geographical differences in the Gaelic language, e.g. Gall Gaidel, Gall Gaidhel, Gall Gaidheal, Gall Gaedil, Gall Gaedhil, Gall Gaedhel, Gall Goidel, Gall Ghaedheil etc. The modern term in Irish is Gall-Ghaeil or Gall-Ghaedheil, while the Scottish Gaelic is Gall-Ghàidheil.
The people concerned often called themselves Ostmen ( Bokmål: Østmenn) or Austmen ( Nynorsk: Austmenn), meaning East-men, a name preserved in a corrupted form in the Dublin area known as Oxmantown which is derived from Austmanna-tún (Homestead of the Eastmen). In contrast, they called Gaels Vestmenn (West-men) (see Vestmannaeyjar and Vestmanna).