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Incandescent bulbs use a metal wire heated by electric current until it emits light. These are inefficient and produce more heat than light for the energy consumed. The lamps also have a short lifetime. But they are very cheap to make.
The fluorescent lamp relies on an electric discharge in a gas. This may emit visible light (as in those pretty neon lamps) or maybe invisible ultra-violet radiation which a suitable coating on the inside of the lamp absorbs and then emits as visible light - the colour can be of a wide range depending on the material used. This lamps need complicated electronic circuit and so are about 10 times the price of the incandescent lamps. But these last 10-20 times longer and use only about a fifth as much electric energy for the same amount of light.
Both lamps come in similar size and format - they can be used interchangeably in standard screw and bayonet sockets.