Cognac & armagnac are different regions of France. Briefly, the Armagnac region started distilling brandy earlier than Cognac but failed to achieve the fame and success of Cognac.
All cognac and armagnac are brandies but not all brandies are cognac and armagnac.
Only brandy made from the cognac region of France can claim to be cognac.
Only brandy made from the armagnac region of France can claim to be armagnac.
Other than cognac and armagnac, many other regions of the world produces brandy but they have yet to acheive the quality and fame of cognac. This is owing the the fact that the climate and soil conditions of cognac is indisputably the best in the world for the growing of grapes used to make cognac. In addition to that, the French law ensures that the quality of cognac made is consistently high, coupled with the skills and experience of the manufacturers located within cognac.