The difference
Rum, citrus, sugar and soda in both. The Mojito muddles fresh mint with lime and sugar; the Rum Collins skips the mint and uses lemon as well as lime, for a plainer, sharper rum cooler.
By the numbers
The Mojito uses mint where the Rum Collins uses lemon juice; both have white rum, lime juice, sugar and soda water. In parts, a Mojito is 2¼ rum, 1 lime, ¾ sugar and 3 soda; a Rum Collins is ¾ lemon, ¼ lime, ¾ rum and 1 soda. By volume, the Mojito is 44% mixer and juice, 33% spirit, 14% citrus and 9% syrup and sugar; the Rum Collins is 35% mixer and juice, 35% citrus, 26% spirit and 4% syrup and sugar.
The Mojito is the stronger drink in the glass (13.1% ABV against 10.1%), but being smaller it holds about the same alcohol (1.01 standard drinks each). Calories are close (about 136 and 129), but the Mojito has more sugar (8.3 g against 5.4 g). Both are built and served in a highball.