At times, we all have considered a simple flow over a rough surfaced flat plate to be the same as a flat plate moving through (cutting through) static air; with exact same relative velocity.

Which is true dynamic wise. and also true from relative motion point of view. But i've heard that the turbulence caused by a simple air flow, over a flat plate (with friction) is slightly different to those caused by a flat plate moving with that exact speed through static air. (i.e the relative motion is the same, but the turbulence caused is slightly different ( eddy's & vortex generation and transport ) )

Does anyone know why this happens?

Why should'nt the two cases be exactly the same?