This question came up recently in another post, and Elkimmeg pretty much had the final word when he quoted the official description of a boiler as an appliance that heats water or produces steam. A furnace, by that same definition, heats air. I finally got into the right frame of mind over the weekend to think about this some more, and came up with the following definitions that I think work for most of us: Boiler: Not exposed to living space. Heats and distributes water or steam to living space. Furnace: Not exposed to living space. Heats and distributes air to living space. Stove: Exposed to living space. Heats air. That's it.