The difference, by the numbers
Both have lemon juice and simple syrup. Only the Gunshop Fizz has Peychaud’s bitters, strawberries, cucumber, citrus peel and Sanbitter; only the Long Island Iced Tea has vodka, tequila, white rum, gin, triple sec and cola. In parts, a Gunshop Fizz is 2 Peychaud’s bitters, 1 lemon, 1 syrup and 2 Sanbitter; a Long Island Iced Tea is ½ vodka, ½ tequila, ½ rum, ½ gin, ½ triple sec, ¾ lemon, 1 syrup and 1¼ cola. By volume, the Gunshop Fizz is 33% mixer and juice, 33% spirit, 17% syrup and sugar and 17% citrus; the Long Island Iced Tea is 35% spirit, 23% mixer and juice, 18% syrup and sugar, 15% citrus and 9% liqueur. That makes them close cousins on the ratio map.
The Long Island Iced Tea is the stronger drink in the glass (16.4% ABV against 7.7%) and holds more alcohol (1.69 standard drinks against 1.18). The Long Island Iced Tea has more calories (about 275 against 240), but the Gunshop Fizz has more sugar (29.5 g against 27.0 g). Both are served in a highball; the Gunshop Fizz is shaken, the Long Island Iced Tea built.