To add to the original post, the project was cancelled as part of anticipated wholesale public spending cuts across Scotland which coincided with the onset of the recession, however, some preparatory work did still go ahead such as resignalling, building the platform at Glasgow Central which would service Glasgow Airport Rail Link (GARL) and increasing the line capacity. This was in anticipation that the project would hopefully go ahead at some later date.
The proposed new project isn't a resurrection of GARL itself but rather, includes GARL as a possible option of connecting the airport with the city, an alternative being a tram link from the airport which connects to the railway at Paisley, continuing from there to Glasgow Central. This may or may not incorporate a heavy/light rail system which would allow the trams to share the rails with regular train services. This is part of a joint funding exercise put forward by the Scottish and Westminster Governments which was dependent on the Scottish referendum returning a 'no' vote, and includes a number of other major transport projects in and around Glasgow.
As a frequent user of Glasgow Airport, I'm quite happy with the existing bus service which gets me from the front door of the airport to the centre of Glasgow in around 20 minutes, though as an owner of TS2016 and of the GARL route, which was designed initially for driver training, it is an interesting enough prospect.