That is correct... But it does not refer to everyone one of that family name.. Just refers to the branch of the family that had the tie..

Let's say my name is Wilson (it is) and I live in Texas... and then in Arkansas is another family of Wilson's... ok .... Here in Texas the family I might have ties to is the Gunn's... It will make me a sept of the Gunns.. Over in Arkansas, the predominate family are the MacHinery's.... Those Wilsons are a sept of the MacHinerys... It then becomes a matter of geography.. now change the names and geography to Scotland and that is how it works out..