Most stoves now have a tertiary air inlet, this is a series of holes at the back of the stove that reignites anything that is going up the chimney unburnt, you will see jets of flames coming towards you.
M/fuel stoves have two other air inlet’s, primary air which draws air in through the bottom of the stove under the grid and is used to control the fire, fully open when lighting the fire and reduced as the fire gets going or is established. The top vent is air wash this cleans the screen by burning off carbon, this is usually kept fully open, however it is adjustable. It works when the stove reaches a high temperature by burning off the carbon.
If you put your hand in front of the glass when the fire is fully on, you can feel the heat on your hand increase as you close down the primary air. Slowing down the primary air reduces the amount of air/heat being lost up the chimney!
Wood burners have tertiary air and one other control, called air wash, the same as M/Fuel and cleans the screen by burning the carbon off of the screen but it also feeds the fire, wood is burnt from the top. A good point to mention here is that some chimneys just work slower than others dependant on the chimney positioning or wind in the area.
– William Evans