conquer usually means to take control of a country or city and its people by force.「conquer」通常表示用武力征服並控制（一個地方或一個民族）。
or to defeat sb, especially in a competition, race, etc.或者指擊敗某人，尤指在競爭、比賽等中。
「The king conquered the city and made it apart of his empire.」「國王征服了這座城市，使它成為帝國的一部分。」
「The world champion conquered another challenger last night.昨晚這位世界冠軍又戰勝了一名挑戰者。」
overcome is to to defeat sb/sth or to succeed in dealing with or controlling a problem that has been preventing you from achieving sth."overcome"是指擊敗某人/某物或成功地處理或控制一個妨礙你取得某項成就的問題。
「I overcame my fear of heights and went on an airplane today.」「我克服了恐高症，今天上了飛機。」