The biggest difference is that Cognac is made from grapes and Whiskey from grain, most usually barley. This grain is mixed with yeast and water, distilled, and then aged in oak barrels.
Cognac begins life as fermented grape juice that first turns into wine. This wine is then double-distilled, before also being aged in oak barrels.
Another big difference is that Cognac can only carry the name if it’s produced according to strict regulations. The most important being that it’s made in the Cognac region, in France. Whiskey, on the other hand, can be made anywhere in the world. Although the Scots spell theirs without the ‘e’. So if you’re drinking a ‘Whisky’, this has been made in Scotland.