A.O. Smith Water Products division is a subsidiary of A.O. Smith Corporation. They manufacture water heaters under the following brands: A. O. Smith, State, Reliance, Apollo, Maytag, GSW, John Wood, and American. All of these were once stand alone water heater companies, absorbed by A. O. Smith. Hard to tell at this point to what extend they are still independent in terms of design and manufacture.
The American Water Heater subsidiary, of Johnson, Tennessee, makes water heater under the American brand, and for the international and private label market, under the Pro-Line and US Craftmaster brands. US Craftmaster is identified as the manufacturer for the Whirlpool brand, of recent infamy at Lowes.
If you think this is all confusion, it is the rule, rather than the exception, in industry these days. Try to identify the manufacturer of a Ridgid tool these days!
