In fuel injection, the fuel is forced through a nozzle to release an aerosol that makes combustion easier and more efficient. The bigger the droplets the lower the efficiency because of the time it takes to burn within a particular combustion cycle. It's also important to get good mixing between the aerosol and the air entering the engine, otherwise the combustion efficiency is reduced and you get CO
rather than CO2 being produced, and soot. Look at photos of the early jet planes on take off.
In a jet engine there is a continuous flame, or self sustaining flame as the fuel burns, so once it's lit it stays lit as long as there's a supply of fuel and oxygen. In a piston engine a spark has to be used to ignite the fuel air mixture, except in a Diesel engine where the compression itself forces combustion.
Vaporisation is just the liquid evaporating into a gas/vapor and is nothing to do with combustion.
Note that the aerosol/evaporation is used to keep the engine components cool. The latent heat of evaporation, ie. the energy transferred to the liquid as it converts to an aerosol/vapor means that the injectors do not overheat. This is another reason why aircraft fuel tanks are not insulated. Cold fuel absorbs a lot of heat energy to get up to combustion temperatures.