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.
We have “Vicariates,” according to the diocesan newspaper. Some services are organized around those groupings. For example, we have a diocesan coordinator of Hispanic Ministry (a plainclothes Sister of some kind - nice lady, good Spanish, but ...), and a lay sub-coordinator (Cuban gent, *very* orthodox) for the Charlotte Vicariate.