The glass on the left is what you'd drink brandy out of (cognac being a type of brandy, sort of like how champagne is a wine, and scotch is a whisky, it gets a special name based on where it's made). Ordinarily you'd warm a snifter with hot water from the kettle, select your liquor, then dump the water out and pour your drink. The water warms the glass which in turn causes the liquid to evaporate and making it easier to pick out flavors when you drink. The shape of the glass holds in the alcohol / water vapour which carry aromatics making them easier to smell--smell being about 90% of taste. You'll also see people drinking the glass by "cupping" the bottom of the glass with their hands rather than holding it like a champagne flute. The reason you'd do that is so that your hand keeps the liquid warmer and helps it to evaporate - again improving and intensifying the flavour.
Bonus round: if you pour a glass of brandy then lay the snifter on it's side the liquid should be right to the edge without spilling. Their design makes it easy to know if you're being ripped off (given that even something mid-tier like Remy XO sells for ~$15-20 in a bar, and a higher end drink like Hennessy Paradis will be about ~$150 per glass, that's a useful feature).
The glass on the right is called a 'lowball' or 'old fashioned' glass and is what you'd typically drink whisky, bourbon, etc. from. I've had scotch at maybe 2 or 3 dozen upscale bars around the world and it's always served in that style glass. A few companies have tried to make "whisky glasses" over the years but
Glencairn is the only one to get any type real traction among scotch snobs. You see it at tasting events -- though you'll get all sorts of crazy glasses at those -- and rarely anywhere else. The only time I can recall receiving scotch in a snifter is at a hotel bar, the Fairmont chain is bad for that; which is a bit of a personal shame. It's not unheard of but at least in Western Europe, Canada, and Southern and East Coast USA it would be unusual to receive receive whisky in anything else unless it was a chain restaurant where the staff just doesn't know any better (the kind of place that serves whisky with ice in the glass)