In the manual trans... it is still a flywheel. The mass serves the same purpose to smooth out crank vibration and clutch engagement.
The automatic's "flex plate" is just a very light stamped sheet metal part. It may or may not have a ring gear. (The ring is part of the torque convertor in many setups) The "flex plate" can be light because the TC is rather heavy and will do the same thing for the auto that the flywheel does for a manual.
For some types of racing you may want a real light "flywheel" but in daily driving this is one part or set of parts where you realy want the mass.
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Dr. Ian Malcolm: Yeah, but your scientists were so preoccupied with whether or not they could, they didn't stop to think if they should.
(Jurasic Park)
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