The wind also affects the speed of the aircraft, which leads to the two speeds we use in aviation:
Picture a hot air balloon in the sky – by using a flame, the pilot can control its climb or descent but it can only move forwards when blown by the wind.
So in conditions of nil wind, the balloon will not move forwards.
When the wind starts to blow, the balloon will move forwards with the wind. So the balloon’s groundspeed (speed over the ground) will increase but since the balloon is not moving relative to the wind, its airspeed (speed through the air) will still be 0.
However if you imagine an aircraft in nil wind conditions, it will still be moving forwards since it has power from the engine. With no wind, the aircraft will have the same forward speed through the air as over the ground (airspeed = groundspeed).
If the same wind that pushed the balloon forwards started blowing, the aircraft would get blown forwards with the air. The aircraft’s speed through the air would be the same (airspeed doesn’t change) but because it has the help of the wind pushing it forwards, its groundspeed would be faster than its airspeed (groundspeed changes).