I know it's semantics for some, but technically an automatic transmission uses a flexplate and a manual transmission uses a flywheel. But I hear people call flexplates flywheels all the time. It's not that big of deal to me, but it can get confusing that way.

The difference is that the flexplate is just a thin piece of metal (compared to it's flywheel counter-part) that serves to connect the crankshaft to the torque converter and hold the gear the starter engages to start the car. Whereas a flywheel is much thicker and not only does it have the gear teeth for the starter (like the flexplate) but it has a surface that the clutch contacts when you release the clutch pedal. It works in a similar fashion to disk brakes, with the flywheel being like the rotor and the clutch being like the break pads.

I hope that helps!

Edit:

Here's a flexplate:


Here's a flywheel:

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