Briefly,
a) Hot and warm flare usually is for water vapor laden vent streams that have a lower operating temp limit of say 3-5degC to avoid water vapor from freezing up in the flare header.
b) Cold and dry flare is reserved for dry (almost zero water content) vapor streams whose sources could be operating at less than 0degC
c) HP flare systems usually have max built up backpressures exceeding say 500kpag - this will then impose a lower design pressure limit of say 1000kpag for source equipment, assuming balanced bellows type PSV's are acceptable
d) LP flare systems collect relief, depressuring and operational vents from source vessels with design pressures lower than 1000kpag or so.