I would also say that this can only be German Wings, as the other airline with "German" in the name was a charter Carrier "Germanair" in the 1970's, operating with BAC 1-11 and A300 before being merged with "Bavaria Fluggesellschaft" to "Bavaria Germanair", later being bought by Hapag Lloyd, a charter carrier that still exists.
German Wings was based in Munich-Riem (still the old airport) and operated a couple of MD-83's on domestic and European flights. Their paintscheme was white with a pink stripe and the pink logo on the tail, you should find some pictures at airliners.net.
They were founded in the late 1980's in order to offer an alternative for business travellers, offering only a 2-2 seating with 114 seats, being quite comfortable in contrast to Lufthansa's 737 with the 3-3 seating even in Business Class.
Their problem was however that they had very "unfriendly" times at most airports, with very early departures and very late returns, on top of this Lufthansa rejected to honour their tickets on an interline basis, so that passengers could not rebook from German Wings to LH. This caused a lengthy trial which was won in the end by German Wings, but by then it was too late. They had run out of cash to maintain their operation and had to shut down in 1990 or 1991 if I remember right.
As far as I know Lufthansa bought the name while the aircraft went in different directions. Aero Lloyd took two of them (D-AGWB and D-AGWC) and used them on their new scheduled flights between Frankfurt and Berlin, still in the Business Class seating configuration.
When Aero Lloyd stopped these scheduled flights, the aircraft were converted into the normal charter 2-3 seating.