Paul,
The black wire is "Hot 110" and the red wire is also "Hot 110", together, they "make" 220V.
Either the <span style="text-decoration: underline;">red OR the black</span> wire combined with the white neutral make 110V. You can even reverse the black and red wires from the power cord and the dryer, it won't make a difference. But you can't plug either (black or red) wires from the power cord to the white (neutral) wire of the dryer because that's how you'll damage parts like the timer, motor and lights... And you need to remove the wire that grounds the dryer body to the white wire terminal as grounding on the neutral isn't allowed here in Canada.
If you look at your home breaker panel, you'll see that two 110-120 volts wires enter the panel and one out of two breakers are connected to one side and those between are connected to the other side (except to my knowledge in those stupid Federal Pacific (FPE)/ now Federal Pioneer panels that are still allowed in Canada and sold by Schneider Electric, the company that also sells the good SquareD panels!).
Now, you'll notice that double breakers should have a red and a black wire attached to them. That's how you get 220-240V. The white wires should mostly be attached to the neutral bar which provides 110-120V when combined with either a black or red wire. And then there are the uncovered ground wires attached to the panel itself.
In Canada, there is a strange way to wire some kitchen 110V outlets on double pole breakers. Just like 240V installations. One red wire and one black wire go to each screws of the "hot" side of a 110V outlet (with the tab removed between both) and the white wire goes to the neutral side (without the tab removed). That makes two independent 15 amps 110V circuits on the same breaker with 14-3 wiring. What I don't understand is how the white 14 wire is considered adequate for two 15 amps circuits, but I won't go further as this isn't related to this topic!
I hope my English vocabulary was better! If what I wrote isn't clear, I'll try to explain you better at home!