@bracconiere The dryer cord and plug and the GF cord and plug carry the same voltage. They differ in that the dryer is designed to carry more "current" (or amps or watts or what ever you want to call it) than the GF. That is the reason for the different cord/plug configuration.
220v "only" devices require two separate 120v legs in residential service and can operate without any more wires, just the two legs, although not considered safe. (no grounding) A "neutral" is not needed or used in such a circuit.
In the dryer seniaro, it needs a "neutral" (or a "ground/neutral") for the 120v circuit in the dryer. In a lot of dryers, that includes the drum motor, timer motor, lights etc.
In a 120v circuit there is just one "power" leg and a neutral. Again a ground is not "needed" for operation but employed for safety.
All that said, I am not bringing up any "best practices or code requirements". Those are many and they can vary per situation and local.
Cheers to all,
it's time to start having Birthday libations
and my focus will be of Blue Moon clone nirvana.
Joel B.