The duty of the Cllr is to represent the ward or electoral sub division they were elected (contested or not contested) or co opted to serve. That is indicated on the notice served by the Principal; Authority returning or acting returning officer..
Where did you get the term "Sub warded" from? In some instances a Parish might not be warded . Where I live the Parish is warded, and the ward names and boundaries are exactly the same as those used by for the Principal Unitary Authority. In other instances, a Parish may be warded but the names and boundaries may be unique to the parish. Different names may apply to those used by Unitary District & County Councils. I don't know of any sub ward division other than polling districts.