General

Two words: Regional Identity

I can say re: Florida that North, Central, and South Florida are (physically and culturally) like three entirely different states. Tampa Bay and Miami are separated by nearly 300 miles. You'll find the people are vastly different. Two major metropolitan areas with two distinct sports markets. To say that the two are the same (i.e. they're both Florida) is to compare apples to oranges.

Of course this is not limited to baseball, but professional sports across the board.

As for places like New York and the San Francisco Bay Area, you have a similar concept of regional identity, albeit in a smaller area. New York Yankees and Mets play in two different boroughs (Bronx and Queens, respectively) which like Tampa Bay and Miami are two distinct regions with different populations, cultures, local economies, etc. Same thing with San Francisco and Oakland. Despite being only a bridge apart, the two cities are entirely different.