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Lille Europe and Lille Flandres are the 2 railway stations of Lille. Those are in the same area. It takes approximately 10-15 minutes to walk from one to the other via the Euralille mall.
Not all destinations are served by each station. From Paris, you can reach both. Lille Europe is usually used for Eurostar and Thalys (ie to UK and Belgium).
The closest to Grand Place is Lille Flandres. The shuttle to the airport is between both railway stations, in front of Euralille center.