A CVT is simply a transmission with no fixed gear ratios. It can have any gear ratio between a set minimum and maximum, it has no "steps" like "1st gear, 2nd gear". In other words, it's a transmission type where you could theoretically have the engine spin where it produces the most power (let's say at 5000 rpm) all the time while accelerating. In reality, car CVTs do still have gears, like the Honda Fit which is a 7 gear automatic CVT transmission.
CVT, DSG or the traditional fluid type are all automatics. They just differ in their inner workings. What you're talking about has nothing to do with the inner-working, the paddle like shifters or + - gates on the shifter is simply an interface that lets you override any of the automatic transmissions and select your own gear.
A distinction to make. You could technically have a CVT transmission that you put in "drive" and drive off and you could have a traditional automatic with paddle shifters. Both are unrelated in their function.