The difference, by the numbers
Both have pineapple juice. Only the Hotel Nacional Special has aged rum, lime juice and apricot liqueur; only the Mary Pickford has white rum, Maraschino liqueur and grenadine. In parts, a Hotel Nacional Special is 3 rum, 3 pineapple, 1 lime and ¼ apricot; a Mary Pickford is 1 rum and 1 pineapple. By volume, the Hotel Nacional Special is 41% mixer and juice, 41% spirit, 14% citrus and 4% liqueur; the Mary Pickford is 44% mixer and juice, 44% spirit, 7% liqueur and 5% syrup and sugar. That makes them close cousins on the ratio map.
The Mary Pickford is the stronger drink in the glass (12.7% ABV against 11.4%), but being smaller it holds about the same alcohol (1.08 and 1.15 standard drinks). The Mary Pickford has more calories (about 163 against 140) and more sugar (9.6 g against 6.3 g). Both are shaken and served in a coupe.