There are three types of paddle shifted transmission, the first two having been discussed already:
1. automatic with manual shift control. Still has a torque converter.
2. computer controlled servohydraulic or servoelectric manual transmission where servounits control both the clutch and gearset. In addition to some of the cars mentioned, the Toyota MR2 Spyder was offered with a servo operated manual transmission.
3. dual clutch, dual input shaft maunual transmission with computer controlled servo hydraulic or servoelectric operation.
The third category started appearing in F1 and a few other race cars in the past few years. I don't know if anyone has used one on a (high end) street car yet.
While type 3. seems similar to type 2. there are differences in operation. The gearsets for the two input shafts (R, 1, 3, 5) and (2, 4, 6) can be shifted independently. The computer preselects the next gear based on whether you are upshifting or downshifting. Only one of the two clutches can be fully engaged at any time.
Shifts are accomplished by disengaing one clutch and engaging the other. the only time things get tricky is if you decide to downshift and slow at the end of a hard acceleration sequence. In this case, the computer will wait until the proper gear is engaged.
For example, if you are accelerting in 4th gear, the computer will preselect 5th on the other input shaft. When it comes time to shift, the computer disengages the 4th gear clutch and engages the clutch on the 5th gear shaft.
While accelerating in 5th, 6th gear will then be selected on the other shaft...
I would love to have one of these, but the transmission would cost more than what I paid for my last 5 cars...
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In addition to the above type, drag racers use 4- or 5-speed (Lenco) transmissions with multiple planetary gear boxes in series. A clutch band is used to stop each planetary gear drive separately to change gear ratios. With all 4- or 5- planetary gears sets operating the gear ratio is the product of all the gear sets. As each gear set is locked out the ratio drops. With all 4- or 5- sets locked the gear ratio is 1 to 1.
These are frequently shifted pneumatically using high presure air. Just another example of how to shift a transmision under servo control, but not very practical for the street.