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 John Collins has gin and soda water. In parts, a Gunshop Fizz is 2 Peychaud’s bitters, 1 lemon, 1 syrup and 2 Sanbitter; a John Collins is 3 gin, 2 lemon, 1 syrup and 4 soda. By volume, the Gunshop Fizz is 33% mixer and juice, 33% spirit, 17% syrup and sugar and 17% citrus; the John Collins is 40% mixer and juice, 30% spirit, 20% citrus and 10% syrup and sugar. That makes them close cousins on the ratio map.
The John Collins is the stronger drink in the glass (10.9% ABV against 7.7%), but the Gunshop Fizz is the bigger drink, so it holds more alcohol (1.18 standard drinks against 1.01). The Gunshop Fizz has more calories (about 240 against 142) and more sugar (29.5 g against 10.0 g). Both are served in a highball; the Gunshop Fizz is shaken, the John Collins built.