The difference, by the numbers
Both have orange juice. Only the Blood and Sand has Blended Scotch, cherry liqueur and sweet vermouth; only the Paradise has gin and apricot liqueur. In parts, a Blood and Sand is 1 Scotch, 1 cherry, 1 vermouth and 1 orange; a Paradise is 2 gin, 1¼ apricot and 1 orange. By volume, the Blood and Sand is 25% mixer and juice, 25% spirit, 25% fortified wine and bitter and 25% liqueur; the Paradise is 46% spirit, 31% liqueur and 23% mixer and juice. That makes them close cousins on the ratio map.
The Paradise is the stronger drink in the glass (15.5% ABV against 13.2%), but the Blood and Sand is the bigger drink, so it holds more alcohol (1.07 standard drinks against 0.95). The Blood and Sand has more calories (about 155 against 120) and more sugar (12.1 g against 6.3 g). Both are shaken and served in a coupe.