The difference, by the numbers
Both have grenadine. Only the Mexican Firing Squad has tequila, lime juice and Angostura bitters; only the Ward Eight has rye whiskey, lemon juice and orange juice. In parts, a Mexican Firing Squad is 3 tequila, 1 lime and ½ grenadine; a Ward Eight is 4 whiskey, 1 lemon, 1 orange and ¼ grenadine. By volume, the Mexican Firing Squad is 68% spirit, 22% citrus and 10% syrup and sugar; the Ward Eight is 63% spirit, 16% mixer and juice, 16% citrus and 5% syrup and sugar. That makes them close cousins on the ratio map.
The Ward Eight is the stronger drink in the glass (16.7% ABV against 16.2%) and holds more alcohol (1.52 standard drinks against 1.39). Calories and sugar are close: about 172 and 177 calories, 5.6 g and 4.7 g of sugar. Both are shaken; the Mexican Firing Squad is served in a highball, the Ward Eight in a coupe.