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并控制（一个地方或一个民族）。
or to defeat sb, especially in a competition, race, etc.或者指击败某人，尤指在竞争、比赛等中。
“The king conquered the city and made it apart of his empire.”“国王征服了这座城市，使它成为帝国的一部分。”
“The world champion conquered another challenger last night.昨晚这位世界又战胜了一名挑战者。”
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"是指击败某人/某物或成功地处理或控制一个妨碍你取得某项成就的问题。
“I overcame my fear of heights and went on an airplane today.”“我克服了恐高症，今天上了飞机。”