The difference, by the numbers
Both have pineapple juice and lime juice. Only the IBA Tiki has aged rum, amaretto, hazelnut liqueur, Maraschino liqueur, passion fruit purée and fresh ginger; only the Singapore Sling has gin, cherry liqueur, triple sec, Bénédictine, grenadine and Angostura bitters. In parts, an IBA Tiki is 2 rum, ½ amaretto, 1 passion fruit, 3 pineapple and 1 lime; a Singapore Sling is 1 gin, ½ cherry, 4 pineapple, ½ lime and ¼ grenadine. By volume, the IBA Tiki is 52% mixer and juice, 26% spirit, 13% citrus and 9% liqueur; the Singapore Sling is 58% mixer and juice, 15% spirit, 15% liqueur, 7% citrus and 5% syrup and sugar. That makes them close cousins on the ratio map.
The IBA Tiki is the stronger drink in the glass (8.7% ABV against 7.7%) and holds more alcohol (1.65 standard drinks against 1.27). Calories are close (about 263 and 265), but the Singapore Sling has more sugar (27.6 g against 20.6 g). Both are shaken; the IBA Tiki is served in a tiki mug, the Singapore Sling in a hurricane glass.