Flashpoint is the temperature the liquid needs to have to give off enough vapour for it to be ignited by some external source like a match. Once those vapours have been burnt the flame goes out.

Firepoint is the temperature the liquid needs to be at to give off vapours at a rate that will sustain a flame once the vapour has been ignited by an external source.

Autoignition is the temperature the liquid needs to be at have enough heat that no external source of ignition is needed to ignite the vapours.