I think what you're asking about are different types of bishops. In our Diocese of Oklahoma, most of you have probably only experienced one type, so some of the others may be a bit confusing. The primary is the Diocesan Bishop. This is the type of bishop that our Bishop Ed Konieczny is. They are the ecclesiastical leaders of the diocese.
Just prior to that, he was a Bishop Coadjutor. This is a bishop who is elected to succeed a Diocesan Bishop. Bishop Ed was elected to succeed Bishop Robert Moody. In that transitional time, after he was consecrated, he took that title. Once the Coadjutor becomes the Diocesan, the term Coadjutor is dropped.
Another type of bishop is a Bishop Suffragan. This is a bishop elected to assist the Diocesan Bishop and to serve under the Diocesan's direction. In essence, it's a working co-bishop in a diocese but without any right of succession when the Diocesan retires or resigns. Sometimes, Suffragan Bishops are called by another diocese to become their Diocesan Bishop.
Some diocese have an Assistant Bishop. This is someone who is already a bishop that is appointed by the Diocesan Bishop to serve under the Diocesan's direction. Sometimes it may be a retired Bishop who becomes an assistant.