No commercial airline will be using FlightStar (or FlightMap for that matter) for operational flight dispatch. FlightStar is for General Aviation or private use only, FlightMap for corporates.
The current market leader (in terms of customer numbers) is Jeppesen with their JetPlan solution followed by SITA and their GraFlite solution.
Also out there is;
Lufthansa Systems with LIDO (the daddy of them all in terms of price!),
EDS with Pheonix (old and TypeB based) and more recently axsFlightPlanning (a great improvement but someone should tell EDS that the 'axs' prefix stands for Atraxis),
Airdata with AirPlan (the low cost carriers favourite),
Navtech with DispatchPro (went through some tough times, but seems to be fighting back),
Air Support with PPS (small Danish company focussed on Corporate Flight Dept's, General Aviation and Military transport ops)
European Aeronautical Group with RODOS (used to be SAS Flight Support and is well respected)
and, last buit not least, Sabre Inc with AirPath (no comment)
All the above have websites that are relatively easy to find for further research.
A few of the nationals also have solutions they developed for themselves and now don't actively market to other carriers like Air France and Iberia. You will find these sometimes still in use in Africa and South America respectively but are rare nowadays.
I think that is it, but I'm sure someone out there knows of other, more obscure, providers supplying product.
Whooaahh!!!