Hi All - There was a spell where a small battery driven bus ran from the station to the Terminal. The Arriva Durham County express bus was called the 'Sky Express' pic:
Arriva North East: 1762 NK05GVZ Dennis Dart SLF/Alexander | Flickr - Photo Sharing! Even after the renaming of the airport the train station has remained as Teesside Airport to this day. Cheers.