from Stevely
I think a building society in the US is a Savings and Loan.
Precisely. These building and loan associations (later S&Ls) became popular at the start of the last century, as very local institutions.

E.g., my grandfather in 1917, among his other functions for the Winona Copper Co. (Chief Clerk for the company and Justice of the Peace for the township), was the manager of the Winona branch office of the Detroit & Northern Michigan Building & Loan Assn. The idea was small savings accounts, which then would be lent for residential housing - not unlike a credit union.

As the 1900s moved on, many S&Ls merged and eventually morphed into full-fledged commercial banks. So, by the end of the century, they added investment and insurance functions. In the era of mergers, some were absorbed by larger giants, who then used the old-fashioned S&L regulators for their own benefit. E.g., AIG was and is "regulated" as an S&L !