If a motor is specified at, for example, 10 oz-in of torque, that means it can provide 10 ounces of force at 1 inch from the center of rotation. If you increase or decrease the distance from the center of rotation you similarly decrease or increase (inverse) the amount of force. E.g., if you double the distance from the center of rotation you halve the force available. Torque = Force * distance. Torque is something of a yes or no question: if I have enough torque I can move it and if I don't I can't. In the case of your car you didn't have enough torque so it just didn't move.
Your helicopter uses gear reduction for two reasons: first because the propeller is aerodynamically limited to how quickly it can spin (before it starts to "stall" -- that's out of scope here
, and secondly to gain more torque. Assuming stall was not an issue, without the gear reduction the propeller would spin up to a certain RPM then not increase any speed because the amount of torque it can provide at that speed will limit it from pushing the blades more quickly.
Why use gear reduction at all -- why not just use a motor with more torque? The issue is that building an electric motor with more torque requires a physically wider motor with more poles and thus it becomes more expensive. It turns out that it's cheaper to produce the motor to spin more quickly and then use gear reduction to gain the torque.