The difference, by the numbers
Both have lime juice and soda water. Only the Mojito has white rum, mint and sugar; only the Ramos Fizz has gin, lemon juice, simple syrup, cream, egg white, orange flower water and vanilla extract. In parts, a Mojito is 2¼ rum, 1 lime, ¾ sugar and 3 soda; a Ramos Fizz is 1½ gin, ½ lime, ½ lemon, 1 syrup, 2 cream and 1 soda. By volume, the Mojito is 44% mixer and juice, 33% spirit, 14% citrus and 9% syrup and sugar; the Ramos Fizz is 46% mixer and juice, 23% spirit, 16% syrup and sugar and 15% citrus. That makes them close cousins on the ratio map.
The Mojito is the stronger drink in the glass (13.1% ABV against 5.9%), but being smaller it holds about the same alcohol (1.01 standard drinks each). The Ramos Fizz has more calories (about 400 against 136) and more sugar (21.1 g against 8.3 g). Both are served in a highball; the Mojito is built, the Ramos Fizz shaken.