Wells Fargo also used to be a SMB B2B oriented bank in the area but basically dropped that practice by the 2000s to concentrate on a mix of IB and Housing that caused it to get acquired by a MN based bank when WF collapsed in 2008.
BoA on the other hand was always much more large business oriented in NorCal.
Also, one last caveat, until the 2000s, Northern California (Bay Area+Sacramento) was always overshadowed by Los Angeles+OC+San Diego. Even today, 2/3 of CA's population lives in SoCal and historically the entire Californian banking industry was largely based there, at least until the Aerospace and Defense Bust after the collapse of the Berlin Wall. VC was always a parochial industry based in R&D heavy but economically backwater regions like Boston and the Bay, while High Finance was concentrated in Los Angeles and NYC.