手掌 (shǒu zhǎng) refers to the palm of the hand as an anatomical part. 巴掌 (bā zhang) also means 'palm' but is more colloquial and often implies the palm used for slapping (e.g., 打一巴掌 'give a slap'). Use 手掌 for neutral or medical contexts, and 巴掌 for informal speech or when referring to a slap.