The four types of camping stoves are solid fuel, unpressurized liquid, pressurized liquid and gas stoves.
Solid fuel stoves run on gel alcohol or hex blocks. The fuel is small, inexpensive and easy to transport, but it can be difficult to find and burns slowly.
Unpressurized liquid stoves use methanol. These stoves are easy to operate, require little maintenance and have cheap fuel, but they also burn inefficiently and can leak fuel.
Pressurized liquid stoves use Coleman fuel, paraffin or gasoline for fuel. The fuel is easy to obtain and burns efficiently, but it is prone to leaking and can flare during cooking, potentially burning the cook and ruining the food.
Gas stoves run on cylinders of compressed gas, such as propane. They are cheap to use and maintain and light to carry, but the fuel can be difficult to find, especially if you are traveling somewhere remote or out of the country.
When choosing a camping stove, you should keep in mind where you plan to use it, how you will transport it, the availability of fuel and the required upkeep. Those factors will help you determine what size and type of camping stove you need.