What are the differences between a dual mass flywheel and a standard flywheel?

The dual mass flywheel is typically misunderstood by a number of people. It's function is not to provide a smooth ride but is actually designed to protect the gearbox from destruction.

My car, a run of the mill Volkswagen 1.9 TDI from twelve years ago, develops a staggering 250ftlb of torque. If this was fitted with a solid flywheel, this is more than enough torque to, if I'm harsh with the throttle and clutch, destroy the gearbox within 20,000 miles.

Because the dual mass flywheel is relatively expensive when compared with solid flywheels that will fit the car, for example from the early VR6 engines on the previous models, I am aware of a number of people within the owners clubs who have opted to go this route when replacing their dual mass flywheel. Typically following this a trashed gearbox follows some months later.

So, the dual mass flywheel is effectively a consumable / sacrificial part designed to prevent the considerable expense of a gearbox rebuild.

Adding to what Nick and Steve have said. Consider the millisecond-by-millisecond operation, and that the rated torque is an average over the engine cycle.

In fact the engine is producing large spikes of torque during each cylinder's combustion event. Rather than transferring this into the gearbox the DMF averages the torque output, reducing the peak and spreading it over a larger range of crank position.

This is of course, good news for drivetrain components.

This chart nicely illustrates my point:

DMF is basically torsional vibration isolator. It does not do anything with damping. It is not damping element. DMF isolates vibrations coming from engine and preventing to reach to gearbox. You may want to look this thesis