How is a regular light bulb different from an energy-saving light bulb?

By "regular" I think you mean a traditional filament (hot wire) bulb. That works by an electric current heating up the wire so that there is visible radiation from it. The problem with that is there is far more radiation (heat (ie infra red), even some ultraviolet) which the eye cannot see, so all that other energy is wasted. So-called energy saving bulbs rely on energy transitions within carefully selected atoms so that it can be arranged that most of the photons are in the visible part of the spectrum.