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Your explanation of how a helicopter flies was very clear. Do you have a similar explanation for what makes a quadcopter, or 6 or 8 motor drone fly in different directions since all the propellers on these drones are fixed and do not tilt?
In the case of quadcopters etc, it is the speed and direction of rotation of each rotor that controls the direction of flight. Quadcopters have two rotors turning in one direction and two in the other, and speeding up different rotors allows variation in the lift, and hence turning or moving in different directions. Horizontal motion is accomplished by temporarily speeding up/slowing down some motors so that the vehicle is leaning in the direction of desired travel and increasing the overall thrust of all motors so the vehicle shoots forward. Generally the more the vehicle leans, the faster it travels. I hope that helps.