英明 (yīngmíng) describes a leader, decision, or policy as 'wise and brilliant' with a tone of authority and far-sightedness — it's used for high-level judgment, not everyday cleverness. 明智 (míngzhì) is the general word for 'wise, sensible' in personal choices; 高明 (gāomíng) emphasizes exceptional skill or cleverness in a specific area (e.g., a doctor or strategy).