The difference
Gin, lemon and syrup in both. The Gin Fizz is lengthened with soda and is tart and dry; the Earl Grey MarTEAni infuses its gin with tea, adds egg white and much more syrup, and is served up.
By the numbers
The Earl Grey MarTEAni uses egg white where the Gin Fizz uses soda water; both have lemon juice, simple syrup and gin. In parts, an Earl Grey MarTEAni is 1 lemon, 1¼ syrup and 2 gin; a Gin Fizz is 1½ gin, 1 lemon, ¼ syrup and 1 soda. By volume, the Earl Grey MarTEAni is 46% spirit, 31% syrup and sugar and 23% citrus; the Gin Fizz is 39% spirit, 26% mixer and juice, 26% citrus and 9% syrup and sugar.
The Gin Fizz is the stronger drink in the glass (10.9% ABV against 9.6%), but being smaller it holds about the same alcohol (1.01 standard drinks each). The Earl Grey MarTEAni has more calories (about 192 against 130) and more sugar (19.2 g against 6.9 g). Both are shaken; the Earl Grey MarTEAni is served in a martini glass, the Gin Fizz in a highball.