Aerodynamics of a Propeller
The NOAA National Weather Service Glossary defines relative wind in a way that might help you make sense of this:


  Relative Wind: The wind with reference to a moving point. Sometimes called APPARENT WIND.


From the diagram in the linked question, you can see that the relative wind is a vector opposite the propeller's 0 degree angle of attack. Simplified, this relative wind is the speed the wind would appear to flow if the air was moving, instead of the propeller. But since the propeller is moving and not the air, we call it relative wind: relative to the propeller, the air is flowing over it because the propeller is moving. 

However, I'm sensing from your question that you might think there is only one relative wind vector, and that is the one parallel and opposite direction to the 0 degree angle attack of the main wings.  However, the as you can see from the definition, any moving point is going to have relative wind!

Remember that relative wind is just the wind in reference to a moving point. So once the airplane is in forward motion, even though the air in the propeller's plane of rotation is no longer still, the relative wind that the propeller "feels" is still coming from the same direction as before, but the magnitude may be modified by the change in the actual speed of the air in the propeller's plane of rotation. Then to get the strength of the relative wind on the propeller, you'd need to add the wind vector caused by the forward motion.

At the risk of over-explaining, remember it's relative wind. Rather than the air blowing (creating wind), the object is moving, so the wind is relative to the moving object.