Without reading all the linked manuals, I will try to answer your question. Control circuits come in a few forms, but two major types are "input voltage" and "contact closure".
For instance, for a typical air conditioner to turn on, you need to apply 24 volts across the terminals for its relay to make it turn on. This voltage is supplied by an external transformer. You can't just hook up a basic switch to the unit and make it turn on and off. You have to supply an external voltage. This is probably also the case in commercial entry doors that use a solenoid device to open a latch.
The contact closure control is another major type and is usually what garage door openers use. If you take the two wires going to your garage door button and touch them together (just like the switch does), then the door opens. You're not supplying a voltage - just connecting a wire momentarily.
When your doorbell system refers to "zero potential" its talking about a simple contact closure that doesn't supply voltage. Connecting the "Electric Door Opener" wires to terminals 20 and 21a of your garage door opener should do what you want. To test this, you could power up the doorbell and use the door opener function while measuring continuity between the two electric door opener wires. They should be normally open and should have continuity briefly when the door open command is sent.
Terminal 5 on the garage door opener is used to supply a voltage to something like a lighted button or some other "smart" controller that needs power to operate.