The difference, by the numbers
Both have lime juice and grenadine. Only the Mexican Firing Squad has tequila and Angostura bitters; only the Pink Lady has gin and Calvados. In parts, a Mexican Firing Squad is 3 tequila, 1 lime and ½ grenadine; a Pink Lady is 1 lime, 1 gin and 1 Calvados. By volume, the Mexican Firing Squad is 68% spirit, 22% citrus and 10% syrup and sugar; the Pink Lady is 64% spirit, 32% citrus and 4% syrup and sugar. That makes them close cousins on the ratio map.
The Mexican Firing Squad is the stronger drink in the glass (16.2% ABV against 15.4%), but being smaller it holds about the same alcohol (1.39 and 1.35 standard drinks). The Mexican Firing Squad has more calories (about 172 against 154) and more sugar (5.6 g against 2.9 g). Both are shaken; the Mexican Firing Squad is served in a highball, the Pink Lady in a coupe.