The difference, by the numbers
Both have Jamaican rum and lime juice. Only the Don’s Special Daiquiri has white rum, passion fruit syrup and honey syrup; only the Planter’s Punch has sugar cane juice. In parts, a Don’s Special Daiquiri is 2 rum, 1 rum, 1 passion syrup, 1 lime and 1 honey; a Planter’s Punch is 3 rum, 1 lime and 2 cane juice. By volume, the Don’s Special Daiquiri is 50% spirit, 33% syrup and sugar and 17% citrus; the Planter’s Punch is 50% spirit, 33% syrup and sugar and 17% citrus. That makes them close cousins on the ratio map.
The Planter’s Punch is the stronger drink in the glass (16.0% ABV against 12.5%), but being smaller it holds about the same alcohol (1.01 standard drinks each). The Don’s Special Daiquiri has more calories (about 172 against 124) and more sugar (18.0 g against 5.4 g). The Don’s Special Daiquiri is blended and served in a goblet; the Planter’s Punch is built and served in a rocks glass.