All fires obviously produce woodgas. The distinction between a woodgas stove and a hobo type stove (normal fire, complete combustion) is that the produced gas is burnt remotely from where it is produced. This seperation can be very small in terms of time and distance, but must be present. Its this seperation that distinguishes a 'Woodgas' stove from other types. Woodgas is full of very volatile subtances including the magic Hydrogen, which offers much greater flame speed than burning char and thus greater heating power and efficiency. An efficient Tlud can be incredibly clean burning.
When wood is burnt in an oxygen controlled environment, char is produced (think charcoal making), releasing flamable volatiles(smoke). When the smoke is burnt remotely, it leaves some char (up to 50% of the original fuel)) which can then be burnt aswell. In effect, this is burning the wood twice. Whether the flame is pre-mixed or diffuse has no effect on the terminology.