It's all the same fire rather open camp fire or closed up in a wood burner.
The only reason you need kindling to start a fire (sticks, paper, leaves) is to make enough heat to start the logs burning really. You all ready have that in those glowing embers (hot coals). The fire is all ready burning your just adding more fuel to it when you toss in the new log. You just close the damper on the wood burner to adjust the air/oxygen the fire is getting to control the speed of the burn.
" but on any normal fire, there is no way you are going to make a fire out of embers and a log. You need newspaper or kindling, or anything that easily combusts. "
You are mistaken there. By embers I geuss you mean hot coals after the other logs have burned down. Any open fire like a camp fire will do the same thing. Burn some logs till they are down to just alot of hot coals and toss in a couple of dry logs. Really dry pine is a good example or oak. Pine will often almost start burning soon as you toss it in, oak my sit a minute or so. Fresh cut wood will be wet and may be hard to burn.
Also in the wood burner the heat is contained in a smaller area somewhat and that will bake the log faster than an open fire of the same size will. An open fire just lets the heat out any direction as fast as it wants to go. In the wood burner the heat can only get out as fast as it can radiate through the sides or flow up the exhaust, so the log is actually surounded by more heat than an open fire. That may help the log to start faster. Sort of like frying something on top of a gas stove or baking in the oven. Baking is surounded by heat like a wood burner, frying only has most the heat at the bottom like a campfire some up around the sides.
As mentioned, the heat from the coals drives out the the impurities in the wood. Mostly flamable gases, water as steam, tars and resins ect as smoke. All that is needed is heat to bake out the flamable gas (methane I beleave) and oxygen to let it burn. It needs to be ignited somehow and the hot coals do that normally. With my charcoal maker that was mentioned, I had a 55gal barrel of wood being baked by a hot fire under it. The gas came out the pipe on top away from the fire so it was not burning. I had to lite that gas with a burning stick then it burned with a nice large flame. No air could get into the barrel where the wood was baking so the charcoal could not burn since it had no oxygen.
That's basically all any fire is except the coals burn up also since they are exposed to air. Anytime you see a flame that is the gas burning as it escapes the solid wood peice, the solid wood itself is the glowing hot coals and ashes you end up with. The smoke is steam, tars, resins, that don't burn.
In some cases maybe the gas will not ignite on it's own from the hot coals. Normally there is alot of small little flames flickering inthe coals and that lights the gas. Sometimes however there may just be hot coals and no little flames and the gas still bakes out of the wood it just does not burn. In that case you still have the same fire and burning the wood, but without flames.
Cardboard boxes are a good example. When we have pizza boxes (and others) I toss them in the wood burner. Pizza boxes make great heat for a short time. Most of the time they hit the hot coals and sit a second then burst into flames. The coals bake the gas out of the cardboard and the little flames around the coals light the gas. Sometimes there are no little flames or the gas comes out of the box far enough away from the flames it does not light. I get smoke and charred boxes baked into coal which will glow red and burn away to ash, but no flames. If I stick a match in when that starts to happen I get a nice poof as the gas lights and then I get alot of flames untill all the gas is baked out then the charred boxes glow red till turned to ash.
Another thought to is it's all the same thing, just larger or smaller. A tiny stick is a baby log, or a log is just an over grown stick. Paper or cardboard is just a processed log. They all burn the same way, some just take longer than others.
When I just want the flamable gas quick and don't need charcoal I will probably bake cardboard boxes. They contain lots of the gas are dry and will bake faster and still produce charcoal peices I can use for other stuff.