In California, the "No Trucks" and "No Trucks over x tons" are used to regulate commercial vehicles. The purpose of these signs is usually used by municipalities to regulate commercial trucks from using (mostly) residential streets.
Most of these signs are posted in residential areas that have a "cut through" street designed for residential traffic. They are usually in response to complaints from residents who live there.
There is an exception in the law for delivery trucks that are making a delivery and not using the street as a shortcut. (FedEx, Moving Van)
It has nothing to do with an RV or a pick up truck.