To understand the difference between how a manual and automatic transmission operate the clutch, it’s important to understand what the clutch is and how it works.
A clutch is made of up a flywheel and clutch plate that connect the engine and the transmission respectively and works due to the friction between the two.
When the clutch is not engaged, springs push a pressure plate against the clutch disc on the engine side which then puts pressure against the flywheel. The result is an equal spinning speed for both the engine and transmission input shaft. To make a vehicle stop with stopping the engine, the wheels need to stop separately from the engine. Therefore the clutch is required, to be able to rotate the wheels at a different speed than the engine.
With a manual transmission, when your foot presses the clutch pedal, there is a cable that pushes on the release fork and presses a bearing in the middle of the diaphragm spring. What this does is pull the pressure plate away from the clutch disc, releasing the clutch from the engine and allowing the wheels to spin at a different speed.
When it comes to an automatic transmission, there is more than one clutch. The different clutches are used to engage and disengage various planetary gears powered by hydraulic fluid. This is different from the manual transmission, which relies on the clutch pedal. The level of pressure associated with the fluid determines which clutches are engaged using that same spring concept from the manual transmission. The clutches are locked using evenly spaced ridges that lock into the gears and clutch housing.
dual-clutch transmission offers the function of two manual gearboxes in one. To understand what this means, it’s helpful to review how a conventional manual gearbox works. When a driver wants to change from one gear to another in a standard stick-shift car, he first presses down the clutch pedal. This operates a single clutch, which disconnects the engine from the gearbox and interrupts power flow to the transmission. Then the driver uses the stick shift to select a new gear, a process that involves moving a toothed collar from one gear wheel to another gear wheel of a different size. Devices called synchronizers match the gears before they are engaged to prevent grinding. Once the new gear is engaged, the driver releases the clutch pedal, which re-connects the engine to the gearbox and transmits power to the wheels.
So, in a conventional manual transmission, there is not a continuous flow of power from the engine to the wheels. Instead, power delivery changes from on to off to on during gearshift, causing a phenomenon known as “shift shock” or “torque interrupt.” For an unskilled driver, this can result in passengers being thrown forward and back again as gears are changed.
A dual-clutch gearbox, by contrast, uses two clutches, but has no clutch pedal. Sophisticated electronics and hydraulics control the clutches, just as they do in a standard automatic transmission. In a DCT, however, the clutches operate independently. One clutch controls the odd gears (first, third, fifth and reverse), while the other controls the even gears (second, fourth and sixth). Using this arrangement, gears can be changed without interrupting the power flow from the engine to the transmission.
h/t to howstuffworks.com for the great info!