One difference in Irish and Scottish names:

Ireland-The head of a given family would adopt "Ua" (grandson) followed by the name of an ancestor. i.e. Ua Suilleabhain=> O'Sullivan.

Scotland-surnames were often formed by adding relationships: so James, son of John, son of Donald=>Seumas mac Iain mhic Domhnuill. As the scottish names were anglicanized, Mc or Mac was the accepted form.



P.S. The examples I give are found in James MacKay's "Clans and Tartans of Scotland."