Airspeed vs groundspeed is a common confusion. Another analogy:
Imagine a power boat moving along a lake ie still water. The boat's speed through the water matches its speed past the shore/ground and is constant for a given power setting.
Now put the same boat at the same power setting moving upstream in a river. The boat's speed through the water will be unchanged. It's speed past the ground, however will now be slower due to the body of water - & the boat imersed in it - moving in the opposite direction. This is exactly the same situation as walking the wrong way along the slidewalk.
If this seems odd, think of something floating in the lake or floating with the current in the river. You don't wonder why it should have a groundspeed even though it's speed through the water is zero (floating with the current, remember).
Similarly to this 'headwind' example, if the boat turns around & cruises downstream then its groundspeed will be faster than its waterspeed.
If it cruises across the current then its ground speed will be the vector sum of its waterspeed *and* the current ie a triangle of velocities.
NOTE: The direct head- or tail-current plus waterspeed is also a vector addition. It's just a special case where the all the directions happen to be aligned so simple addition or subtraction works.