The difference between a formal and a vernacular region is that

The difference between a formal and a vernacular region is that one of them is defined by same or similar characteristics, usually physical, while the other is defined as a set of cultural identification.

The formal region represents a region in which all of the people in it share one or more distinctive characteristics.

The vernacular region represents a region in which the people living in it collectively consider themselves as interconnected by sharing mutual identity, culture, history...