Nashville has experienced really rapid growth too over the last 20 years, and I think it takes a while for naming conventions to catch up. Given by the fact that what people call suburbs appear to you (as I'm assuming, a relative newcomer) to be "inside the city".

My own hometown has experienced rapid growth over the same time span as Nashville, and has annexed large portions of what were commonly known as the suburbs. So there has been a literal change from what used to be suburbs to now be within city limits, in the course of a generation.