摇摆 covers both physical swaying (e.g., a tail) and metaphorical wavering (e.g., indecision). For physical motion, 摇晃 (huàng) is more about shaking or rocking, while 摇摆 implies a back-and-forth swing. For indecision, 摇摆不定 focuses on vacillating between options, whereas 犹豫不决 and 举棋不定 emphasize hesitancy or inability to decide.