In some instances Irish families have Scots roots and vice versa. In my own case, the original stock migrated from Ireland to Argyll right around the 10th or 11th century, became wealthy, landed (built the oldest standing stone castle in Scotland--Castle Sween), and then, on the wrong side at Bannockburn, went back to Ireland. In fact, there are, today, reportedly more MacSuibhne's in Ireland than there are in Scotland although the name (in that form and that spelling) originated there. But, as I understand it, the "O" in "O'Conghaile" is roughly analogous to the "mac" in "MacSuibhne." Both of these prefixes mean "son of" according to my information. Maybe the original Conghaile was a Scot or related to a Scot before it became the convention to add "Mac" or "O" to designate lineage?

Just a thought...