A houseboat (different from boathouse, which is a shed for storing boats) is a boat that has been designed or modified to be used primarily as a home. Some houseboats are not motorized, because they are usually moored, kept stationary at a fixed point and often tethered to land to provide utilities. However, many are capable of operation under their own power.
you are correct in the definition of a floating home and a houseboat in California. The Lozman decision by the US Supreme Court gave us a federal legal definition of a floating home. Before the Floating Home laws the BCDC determined who could be a marina with floating homes, at the time called "Houseboats".