There are 4 common types of flat roofs.
A Non Insulated Roof has no insulation and is typically something like a garage where you have the structural deck and the waterproofing goes directly onto this deck. This can only be used for buildings that have no heat in them. If the building is heated there are regulations on renovations and new build that have to be met for u-values.
A Cold Roof is one of the most popular ways to insulate a roof as the insulation goes between the rafters / joists in the roof. A cold roof isn't as easy to get the same u-values as a warm roof or inverted roof as the wooden joists and rafters aren't as good at insulating as the insulation is. The build up is waterproofing layer directly onto the deck with insulation below with a vapour barrier attached to the joists with a ceiling installed below. They usually have an air gap between the insulation and deck for ventilation.
An Inverted Roof is where the insulation is above the waterproofing layer. It is typically something like a balcony where you have the structural deck, then the waterproofing membrane directly onto this deck, then an Extruded Polystyrene protects the waterproofing before paving or decking. This allows regular access to the roof. So no vapour control layer is needed as the waterproof membrane is on the warm side of the insulation acting as both the waterproof layer and the vapour control layer.
The vapour control layer is there to prevent warm moist air from the inside of the building meeting cold air from outside. If the moisture in the warm air was to meet the cold air this would form condensation at the dew point (usually at about 3 degrees celsius) This will occur within the insulation layer and without a vapour control layer being present would cause condensation to form which would eventually lead to the timbers starting to rot.