The difference, by the numbers
Both have triple sec. Only the Between the Sheets has white rum, Cognac and lemon juice; only the Margarita has tequila and lime juice. In parts, a Between the Sheets is 1 rum, 1 brandy, 1 triple sec and ¾ lemon; a Margarita is 2½ tequila, 1 triple sec and ¾ lime. By volume, the Between the Sheets is 55% spirit, 27% liqueur and 18% citrus; the Margarita is 59% spirit, 23% liqueur and 18% citrus. That makes them close cousins on the ratio map.
They are about equally strong in the glass (18.7% and 18.8% ABV), but the Between the Sheets is the bigger drink, so it holds more alcohol (2.03 standard drinks against 1.58). The Between the Sheets has more calories (about 233 against 179) and more sugar (8.0 g against 5.3 g). Both are shaken and served in a coupe.