Incense Stick vs Candle
In a candle, the wax first melts, then turns into a vapor above the wick and the oxidation region, where the vaporized fuel mixes with air, surrounds the central, cooler region. You can demonstrate this by extinguishing a candle and then relighting the smoke above the candle... the flame will flash back to the wick. This "flash-back" can be hazardous in a lab using ether, since a nearby flame can ignite the fumes which will burn back to the ether can.

Incense, smoldering cotton and similar combustion relies on thermal degradation of a solid, producing a narrow flame-front on the surface of the solid fuel. Since oxygen cannot penetrate the solid, the rate of combustion is limited. For that reason, cotton bales burn slowly but are very difficult to extinguish, since the interior remains hot and water cannot quickly penetrate. On the other hand, stretching a cosmetic cotton ball changes the burning from smoldering to an intense flame.