We have one. He’s a relict of the previous Bishop, and he often goes on Diocesan-sponsored cruises and tours. He also visits parishes and gives pep talks about the building fund. Nice man, speaks Spanish ... but I think he may not be really orthodox, since the current Bishop has him doing glad-handing instead of really running anything.
Churches are also collected to what is called deaneries in the Eastern U. S. The Dean of the Diocese would then equal the Vicar General. And each local group of churches would have a Dean also.
Instead of deaneries, I would gurss that most Catholic Diocese have vicariates. The local collections of churches in the West have a vicar rather than a dean.