Those lifting for size will usually work for the "pump," which is when blood brings oxygen and nutrients to your muscles and gives you a sort of high. The type of lifting done by bodybuilders is meant to create microscopic tears in the muscle, forcing the body to repair the muscles and expand the storage capacity. The repairs caused the muscles to grow larger, a process known as hypertrophy.
When the muscles grow larger, they are able to hold more energy, which means they can exert greater force. However, the energy stored in bulky muscles is not the same as real strength, and bodybuilders often tend to be weaker than they look.
The term "bodybuilding" usually refers to competitive exhibitions, and a lot of "bodybuilders" are only working out to get the kind of body that will look good on a stage.