The difference, by the numbers
They have no ingredient in common: the Kentucky Buck has strawberries, lemon juice, simple syrup, bourbon, Angostura bitters and ginger beer, the Mojito white rum, lime juice, mint, sugar and soda water. In parts, a Kentucky Buck is ½ lemon, ¼ syrup, 1 whiskey and 1 ginger beer; a Mojito is 2¼ rum, 1 lime, ¾ sugar and 3 soda. By volume, the Kentucky Buck is 38% mixer and juice, 38% spirit, 14% citrus and 10% syrup and sugar; the Mojito is 44% mixer and juice, 33% spirit, 14% citrus and 9% syrup and sugar. Different bottles, similar balance: that makes them close cousins on the ratio map.
The Mojito is the stronger drink in the glass (13.1% ABV against 11.4%), but the Kentucky Buck is the bigger drink, so it holds more alcohol (1.56 standard drinks against 1.01). The Kentucky Buck has more calories (about 222 against 136) and more sugar (16.4 g against 8.3 g). Both are served in a highball; the Kentucky Buck is shaken, the Mojito built.