I'm currently reading Brian Boru, King of Ireland, written by Roger Chatterton Newman and re-published in 2011 by Mercier Press.  Reading about Brian Boru led me to contemplate Dál gCais, also known as "The Tribe of Cas" or the Dalcassians.  I believe my husband's Hickey ancestors (the O'Hickeys) belonged to Dál gCais.  

So what's the difference between clans and septs?  In ancient Ireland, the population was small, and mass movement of people was uncommon.  A person could be known by only one name (e.g., Niall, Eoin, Art) since it was unlikely there was anyone else in the locality with the same name.  Irish society was organized around traditional kinship groups or clanns.  Consequently, a first name and a clann/clan name was sufficient identification. The clanns traced their origins to larger pre-surname population groupings such as Ui Briuin in Connacht, Dal gCais in Munster, and Ui Neill in Ulster. The Gaelic Clann system was well established and gave people a common identity with their tribe and with the commonly-shared area. The single name system began to break down during the eleventh century as the population was growing and there was a need for a further means of identification.  

Quoting a Wikipedia article:  "Scholars sometimes disagree about whether it is better to use the terms "sept" or "clan" when referring to traditional Irish family groups. Historically, the term 'sept' was not used in Ireland until the nineteenth century, long after any notion of clanship had been eradicated. It is often argued that the English word 'sept' is most accurate referring to a sub-group within a large clan, especially when that group has taken up residence outside of their clan's original territory. (O'Neill, MacSweeney, and O'Connor are examples.) Related Irish septs and clans often belong to larger groups, sometimes called tribes, such as the Dál gCais, Uí Néill, Uí Fiachrach, and Uí Maine. The late Edward MacLysaght suggested the English word 'sept' be used in place of the word 'clan' with regards to the historical social structure in Ireland, so as to differentiate it from the centralized Scottish clan system. This would imply that Ireland possessed no formalised clan system, which is not wholly accurate. Brehon Law, the ancient legal system of Ireland, clearly defined the clan system in pre-Norman Ireland, which collapsed after the Tudor Conquest. The Irish, when speaking of themselves, employed their term 'clan' which means 'family' in Irish."

In each clan, there tended to be one sept (division) which became more powerful than others through war and politics. The leaders were accorded royal status in Gaelic Ireland. Some of the more important septs to achieve this kind of power by the 2nd millennium were O'Conor in Connacht, O'Neill of Clandeboy in Ulster, and O'Brien of Thomond in Munster. The O'Briens descended from Brian Boru.