As others have pointed out, it’s done with independently variable thrust, i.e. Making the propellors turn at different speeds, causing the drone to tilt in one direction.
This is also why 4 (or more) propped drowns are so dominant: using this system you can have the drone move in all 6 degrees of freedom without needing a single movable part (aside from the rotors themselves obviously)
While hovering, it is exactly how you described. But when going forward, the rear rotors speed up and the whole drone pitches forward a bit. Usually the drone has some sensors to measure the angle and holds it automatically. Because it is no longer level, the drone now flies forward and downward. The downward motion can be countered by increasing the rpm on all 4 motors simultaneously
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