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there is a huge difference between both.
VAV : Variable Air Volume
automated damper box controls the quantity of air passing to a specific area , exists in AHU's System
VRV : Variable refrigerant volume
Central Condenser units that controls more than one indoor unit , its a closed DX system
VAV stands for veritable air volume which controlls the flow of air volume and VRV is stands for variable refrigerant volume which controlls the flow of refrigerant in refrigerant piping system in direct expansion system
I believe the answer by Mr Muhammad is enough .