The difference, by the numbers
They have no ingredient in common: the Hotel Nacional Special has aged rum, pineapple juice, lime juice and apricot liqueur, the Passion Fruit Martini vanilla vodka, passion fruit liqueur, passion fruit purée and vanilla sugar. In parts, a Hotel Nacional Special is 3 rum, 3 pineapple, 1 lime and ¼ apricot; a Passion Fruit Martini is 1 vodka, ½ passion liqueur, 1 passion fruit and ¼ sugar. By volume, the Hotel Nacional Special is 41% mixer and juice, 41% spirit, 14% citrus and 4% liqueur; the Passion Fruit Martini is 38% spirit, 37% mixer and juice, 15% liqueur and 10% syrup and sugar. Different bottles, similar balance: that makes them close cousins on the ratio map.
They are about equally strong in the glass (11.4% and 11.0% ABV), but the Passion Fruit Martini is the bigger drink, so it holds more alcohol (1.52 standard drinks against 1.08). The Passion Fruit Martini has more calories (about 235 against 140) and more sugar (21.1 g against 6.3 g). Both are shaken; the Hotel Nacional Special is served in a coupe, the Passion Fruit Martini in a martini glass.