Camping stoves come in two basic types: propane (or sometimes butane) or liquid fuel. They are usually single burner units although dual and even triple “suitcase” stoves are available.
Propane stoves currently dominate the market due to simplicity, inexpensive design, minimal smell and widespread retail availability of propane bottles.
Liquid-fuel pressure stoves run on compressed liquid fuel of some kind, traditionally Coleman fuel or unleaded. They were the default stoves for decades before the rise of propane. Pressure stoves typically cost less to run1), put out more BTU in a smaller package. The tradeoff is smellier fuel than propane and more complexity than the “turn the knob and light a match” starting procedure seen in propane gear.
There are other, sometimes more exotic fuels often used used by backpackers who watch their grams. Every Road Leads Home reminds us that it is possible to cook on a Buddy heater.2)
Another popular countertop stove is the Coleman propane stove pictured right.
Since countertop stoves are relatively wide some 'dwellers opt for slimmer camping models.
Propane camping stove burners frequently mount directly to the top of the 1# bottle. This makes for light weight and easy storage, but can also be top-heavy and unsteady.
Pressure stoves can be more squat and steady as they don't have to work around the inherent height of the propane bottle.
Note that some compact stoves can overheat their fuel tank if too wide a pan is used:
It affects any stove that has the burner and fuel tank close to each other, which is common in small, portable, or backpacking singleburner stoves. The reason wide pans are deprecated is that they reflect more heat back onto the tank/font. Taller, narrower pots will help the stove run cooler if it is prone to overheating.4)
Electric stovetops are generally used by folks who use campsites with electric hookups. Resistance and induction cooking both use 1000-2000w watts of power to run each “burner” although the induction unit will be ~12% more efficient.5)