As I understand it, in Irish genealogy race refers to the descendants of a common ancestor. A clan was essentially all those members of a common ancestor living in a particular area who owed allegiance to the clan chief. A large clan could contain septs, which were essentially family groups within the clan who owed allegiance to the sept chief, who owed allegiance to the clan chief. Some septs could be also be clans, as they contained another layer of septs below the sept chief, the sept chief would be the clan chief for the smaller septs whose chiefs owed allegience to the sept chief, who in turn owed allegiance to the clan chief. Much confusion arises because the modern use of surnames largely post-dates the clan system, but many modern surnames are based on the old clan and sept names.
In your example, the Thomonds and Hurleys would have considered themselves to be descended from an individual named Blod. Thomond would be the clan, and Hurley the sept, which can also be considered a clan in its own right.
Clan Donald USA