Both Cognac and Armagnac are grape brandies, traditionally aged in oak barrels before bottling, but the differences are huge. As Ben says, Cognac is produced in the Charente, not far from France’s west coast and a little way north of Bordeaux. Armagnac, however, is produced in Gascony, where the climate is much more continental and noticeably warmer in summer, and the vineyards are substantially protected from the Atlantic by the huge Landes forest.
The soils are also very different, with arguably the finest Armagnac grapes grown on the ‘tawny sands’ of the Bas-Armagnac sub-region. Grapes – Cognac is more than 95% produced from Ugni Blanc, whereas Armagnac’s vineyards are a mix of Baco 22A, Ugni Blanc, Folle Blanche and Colombard (plus small amounts of a few others).
Cognac is all produced via double distillation – in other words, the wine is run through the still twice, producing (in theory) a spirit of greater strength and – depending on your point of view – one that is finer or more simple. Most Armagnac is produced by single distillation, encouraging greater complexity, but sometimes more ‘challenging’ and even rustic flavours when young. There are a few double-distilled Armagnacs too, often VS or VSOP level.
I could go on – the oak barrels for aging are also different, and the final products in Armagnac are more diverse: traditional designations like VS, VSOP and XO/Hors d’Age, but also age-stated blends (eg 15-year-old, 25-year-old, and – Armagnac’s real USP as there are few Cognacs like this – vintage Armagnacs from one single year.
Armagnac also has Blanche, a white spirit kept for a short time in stainless steel or other inert containers and perfect for cocktails (or drinking frozen with oysters). Essentially a colourless eau-de-vie…
Hope that rather long explanation helps!!