The difference, by the numbers
Both have soda water. Only the Mojito has white rum, lime juice, mint and sugar; only the Tom Collins has simple syrup, lemon juice and gin. In parts, a Mojito is 2¼ rum, 1 lime, ¾ sugar and 3 soda; a Tom Collins is 1 lemon, 2 gin and 2 soda. By volume, the Mojito is 44% mixer and juice, 33% spirit, 14% citrus and 9% syrup and sugar; the Tom Collins is 39% mixer and juice, 39% spirit, 19% citrus and 3% syrup and sugar. That makes them close cousins on the ratio map.
The Mojito is the stronger drink in the glass (13.1% ABV against 11.1%), but the Tom Collins is the bigger drink, so it holds more alcohol (1.35 standard drinks against 1.01). The Tom Collins has more calories (about 150 against 136), but the Mojito has more sugar (8.3 g against 3.5 g). Both are served in a highball; the Mojito is built, the Tom Collins shaken.