In a dish of flammable liquid such as paraffin, a region will exist above the liquid surface in which the evaporating fuel vapour is well mixed with air. If the paraffin is heated above about 40°C, this region will become flammable; the vapour concentration in air is above its lower flammability limit.
The lowest temperature at which this occurs is called the flash point; the liquid temperature at which application of an ignition source will cause a flame to flash across the surface of the liquid.
This is a premixed flame moving through the vapour/air mixture but, just above the flash point, it burns out (or self-extinguishes) because it has consumed all the vapour. If heating is continued, a temperature will be reached at which ignition of the vapours will lead to a flash, followed by the development of a sustained diffusion flame at the surface flame.
This temperature is known as the fire point, the lowest temperature at which the rate of supply of fuel vapours, by evaporation, can sustain the flame.