What is the difference between an open air intake and a cold air intake?

With an open air intake the filter sits exposed in the engine bay. The air takes a short, less winding route to the turbo, which lowers resistance and makes the intake audible. With a cold air intake that same filter is shielded and fed with cool air from outside. In practice the two overlap: a well designed open intake always has shielding, because warm engine bay air undoes the benefit.

Our open air intake for the A6 C8 is designed around exactly this point: a short air path with shielding against warm engine bay air.