The difference, by the numbers
Both have lemon juice, simple syrup and strawberries. Only the Gunshop Fizz has Peychaud’s bitters, cucumber, citrus peel and Sanbitter; only the Kentucky Buck has bourbon, Angostura bitters and ginger beer. In parts, a Gunshop Fizz is 2 Peychaud’s bitters, 1 lemon, 1 syrup and 2 Sanbitter; a Kentucky Buck is ½ lemon, ¼ syrup, 1 whiskey and 1 ginger beer. By volume, the Gunshop Fizz is 33% mixer and juice, 33% spirit, 17% syrup and sugar and 17% citrus; the Kentucky Buck is 38% mixer and juice, 38% spirit, 14% citrus and 10% syrup and sugar. That makes them close cousins on the ratio map.
The Kentucky Buck is the stronger drink in the glass (11.4% ABV against 7.7%) and holds more alcohol (1.56 standard drinks against 1.18). The Gunshop Fizz has more calories (about 240 against 222) and more sugar (29.5 g against 16.4 g). Both are shaken and served in a highball.