What's the difference between a Martini and a Manhattan?

A Martini uses gin (or vodka) with dry vermouth; a Manhattan uses rye (or bourbon) with sweet vermouth and bitters. The Martini garnishes with olive or lemon, the Manhattan with a cherry.

Both are stirred cocktails served up in a coupe, both date to the late 1800s, and both follow the same spirit-plus-vermouth template — but the components and proportions diverge. A classic Martini is 2 to 2.5 oz London Dry gin, 0.5 to 1 oz dry vermouth, stirred 25 to 30 seconds, garnished with an olive or a lemon twist. A classic Manhattan is 2 oz rye whiskey, 1 oz sweet vermouth, 2 dashes Angostura bitters, stirred, garnished with a brandied cherry. The Martini is dry, herbal, and crisp; the Manhattan is sweet, spice-forward, and rich. Vodka has replaced gin in many modern Martinis (a Vesper splits the two); bourbon has replaced rye in many modern Manhattans (rye is sharper, bourbon softer). Both substitutions are accepted variations rather than mistakes.