Nope They're entirely different.
In simpleton terms, CVT is deployed using a pulley system.
A Dual clutch as the name suggests always has 2 gears ready to go (one up and one down) depending on the need for the car.
Watch these youtube videos:
2008 Lancer CVT
DCT Dual Clutch Transmission
The generic evolution has been:
Manual gears -> Basic Auto -> Tiptronic Auto -> CVT -> DCT
So Dual clutch is really the way of the future. CVT is an interim solution.