Well, Cognac is the type of brandy that it is, signifying its geographical source, in the same way that Armagnac is a brandy from further south and Janneau is one brand of Armagnac like Courvoisier and Martell are brands of Cognac. So: generic - brandy, source - Cognac, brand or make - Courvoisier.

Courvoisier, to my palate is sweeter, hence tastes "fuller" but I prefer the relatively dryer Martell. But try Remy Martin or Hine: they are both elegant (and sometimes more pricey) alternatives.

And Armagnac has a touch of prune and smoke to it, made in a slightly different way and from different grapes, soil and climate. Experiment!