Ranges and ovens have different configurations, because they are often set up for even higher amp service than a dryer.
That matter could be dealt with by trading down the breaker for the circuit if you think it’s necessary.
The main point is to get two hot wires to the dryer, one neutral wire, and perhaps one ground wire as well. The ground wire, if connected through, would also connect to the metal frame of the dryer, otherwise the neutral wire does that.
Under no circumstances should a hot wire be allowed to substitute position for a ground or neutral wire. If you don’t know what you’re doing, it could be the last mistake you make.
I see what happened. They changed the standard configuration, and it now requires a ground lug. It would be best to change the cable to ground the appliance. They explain it in that link I posted just above....
Yes, the range draws a heckuvalot more current, and the differences are a lot more than just the plug, the home run has to be a much larger gauge wire than for the dryer run. Both are 220V, so be careful out there. I lived in a house that had a three phase service, that led to strange things in the wiring.