The difference
Both are gin, orange liqueur and lemon. The Corpse Reviver No. 2 pours them in equal parts and adds Lillet Blanc and a dash of absinthe, which make it more aromatic and a little lower in strength; the White Lady is the plainer, gin-forward sour.
By the numbers
Both have gin, triple sec and lemon juice. Only the Corpse Reviver #2 has Lillet Blanc and absinthe. In parts, a Corpse Reviver #2 is 1 gin, 1 triple sec, 1 Lillet and 1 lemon; a White Lady is 2 gin, 1½ triple sec and 1 lemon. By volume, the Corpse Reviver #2 is 25% liqueur, 25% spirit, 25% citrus and 25% fortified wine and bitter; the White Lady is 45% spirit, 33% liqueur and 22% citrus.
The White Lady is the stronger drink in the glass (17.8% ABV against 14.9%), but being smaller it holds about the same alcohol (1.67 and 1.58 standard drinks). The Corpse Reviver #2 has more calories (about 211 against 189) and more sugar (11.0 g against 8.0 g). Both are shaken and served in a coupe.