Are all heaters exactly as energy efficient as each other? I many applications, efficiency is measured in terms of how much of the input energy is wasted generating heat instead of the actual type of energy you want. For example, lightbulbs generating heat instead of just visible light, or an engine generating heat instead of only kinetic energy.
But what about heaters? Would choosing a heater with a fan, blowing air around the room (so that the hot air doesn't just rise straight up to the ceiling) have any difference in the heat output of the device? Given that the heater with the fan would take some of the energy from its heating element to power the fan instead, so that the devices still use the same number of watts. Thermal energy is just kinetic energy, but with motion in many different directions at once, right? So kinetic energy should be a special form of thermal energy? And thus, all heaters should be exactly as efficient, nomatter what nice features they have (such as a fan)?
Are all heaters (same wattage, electric to thermal, no geothermal or other extra energy source) exactly as efficient as each other?
 A: Further to Samuel's answer, beyond pure energy efficiency, another measure of efficiency is how efficiently the heater converts the heat energy it produces into the heat that makes you comfortable.
Cheap electric oil heaters in particular tend to be small for the amount of heat they produce, which makes their surface hotter. This hotter surface causes the air to be strongly heated, which tends to rise as a narrow column to the ceiling, causing a large amount of hot air to be concentrated near the ceiling, with the associated large heat losses.
A larger sized heater that is cooler on the surface will perform better for a given power input output as the convection will not be as strong.
A: 
Are all heaters (same wattage, electric to thermal, no geothermal or other extra energy source) exactly as efficient as each other?

No. Let's focus just on electrically powered heaters. If you have a heater that basically consists of a resistor with a current passing through it, you have 100% efficiency of electrical energy to heat energy conversion. Can't beat that, right? Actually, that's wrong. It is possible to beat that. Heat pumps, which basically 'pump' heat from one place (e.g., the cold air outside your house) to another place (e.g., your living room) can have an efficiency of over 100%, meaning that if you put, for example, 100 Watts of power into the heat pump you might get 300 Watts of heat pumped into your living room - much more efficient than just using that same amount of electricity to heat a resistor.
Heat pumps have to abide by the 2nd law of thermodynamics as well as the conservation of energy, so their efficiency depends on the difference between the "outside" and "inside" temperatures. They work best in climates with relatively mild winters like, say, most of California where the temperatures hardly ever drop below freezing. They probably aren't very popular in places like the Chicago area, though, because the large temperature difference between the outside and inside temperatures on very cold days translates into a rather low efficiency.
