Yes, you're (almost all) right. The fast trains from Brussels to south-of-Paris, e.g., to Montpellier, Nice or Toulouse (and to be absolutely correct, one just to Marne-la-Vallee [Disneyland]), are operated as TGV trains (and run via CDG and Disneyland, rather than central Paris), whereas the winter snow trains from Amsterdam and Brussels to the Alps (not stopping at CDG) are Thalys trains (operated by Thalys? by the Belgian and French railways?). Thanks for the correction.