Let's see:
- Anything produces some infrared radiation. The amount of infrared radiation increases with the amount of heat the object radiates. Even stuff at absolute zero still has molecules that "wiggle" (quantum mechanics uncertainty stuff)
- In the case of a stove burner or anything that works with gas/fuel(wood, coal, et Cetera) the gas is combusted to generate the initial heat and then conducted/convected/radiated. Whereas for electric appliances there are different ways that the heat can be generated:
- For a microwave: A magnetron generates microwaves "tailored" for what you want to heat (food), these make the water molecules in the food "vibrate" or wiggle around which makes the food warm.
- For an electric furnace/electric stove/water heater: Electricity is "sent" through a wire and the electrons make the wire get hot due to friction between the electrons and the conductor (wire), then the heat generated from that is conducted/convected/radiated into whatever is you want to heat.
- Convection/Induction stoves: An electromagnet generates an electromagnetic field that heats up your cooking container(pot, pan, etc...). This happens because a very low-voltage but large current is induced in your cooking-container this current will heat up food but won't electrocute anyone because the voltage is too low to get throw anybody's skin.
- Anything that's hot irradiates heat and infrared light; the hotter, the blue-er until it gets white; then it's over the visible spectrum meaning that the frequency of the light emitted is too high for us to see. Furthermore, different fuel/oxidant compositions when there's combustion can generate different colors of flame because of other effects but for the case of just hot objects, it's always dependent on the temperature.
- Heating with fire and using conduction/convection/radiation is different from the microwave heating I mentioned because when using fire or something that's hot because of the electricity "flowing" through it, you just use the heat from whatever is hot (flame/heating-element) to heat up your food or container with food. On the other hand, for microwave ovens, the microwaves which are actually pretty big (100cm to 0.1cm) (but small compared to radio waves, 100km to 1mm) go through the food and make only the water molecules vibrate. Temperature is related to how fast whatever molecules you're talking about "vibrate". The faster, the hotter the thing you're touching/talking about...
Anyways, microwave ovens are completely safe, as the kind of radiation they produce is called non-ionizing because it cannot break chemical bonds due to the fact that these waves do not carry nearly as enough energy. (to break a chemical bond you need at least 5 eV/bond on average which is figures of magnitude smaller than what a microwave produces!) In other words, it can't do anything other than heat up stuff because it does not produce enough energy, so it just makes the molecules "wiggle" around. The reason why ionizing radiation such as the one produced by radioactive stuff is dangerous in large amounts is because it has enough energy to break chemical bonds, so it can break the bonds in your DNA effectively modifying it/messing it up. But in the case of Radiowaves or Microwaves, it won't even get close to it.