Generally, the nine counties that have contact with San Francisco Bay. Clockwise they are: Contra Costa, Alameda, Santa Clara, San Mateo, San Francisco, Marin, Sonoma, Napa and Solano counties.
The Bay Area is very distinct and unmistakable to those who are familiar with it's culture and lifestyle. Outsiders often don't get it. You can't fake being from the bay. When you say "frisco", you give yourself away. Bay Area people don't say that.
The term Bay Area as mentioned, almost invariably refers to the San Francisco Bay Area. Other regions that carry this name only do so within their local areas. Some other terms heard in the bay area such as "the south bay" are used in a few other places, most notably in San Diego where there is also a south bay.
bay area Contra Costa, Alameda, Santa Clara, San Mateo, San Francisco, Marin, Sonoma, Napa and Solano counties.