We Bruces have never been a "Clan." We are a "Name," "Family," or "House" instead.
The major difference is that all Bruces are considered to be related by blood, however distantly, while the members of a Clan may or may not be actually related by blood.
In addition, the distinction in our case relates to our background being Norman and Lowland scots, rather than Highland Scots.
The Bruces were a long established Family in Scotland long before the formation of most of the Clans.
Thomas Allen Bruce
High Commissioner of the Chief of the Name of Bruce