Definition (Cambridge Dictionary): to take control or possession of foreign land, or a group of people, by force（侧重战胜和控制，书面用词）

Example:

The Spanish conquered the New World in the 16th century.

西班牙人在16世纪征服了新大陆。

The English were conquered by the Normans in 1066.

诺曼人于1066年征服了英格兰人。

He has finally conquered his fear of spiders.

他终于战胜了对蜘蛛的恐惧。

Definition (Cambridge Dictionary): to defeat or succeed in controlling or dealing with something（多指战胜或克服非物质的东西，如困难和不良习惯等。语气较弱也可指在斗争或竞争中战胜或压倒对方）

Example:

Eventually she managed to overcome her shyness in class.

她终于克服了上课时的羞怯。

20,000 demonstrators sang "We shall overcome" as they marched through Washington.

两万名示威者高唱着“我们会胜利”在华盛顿街头游行。

Definition (Cambridge Dictionary): to win against someone in a fight, war, or competition（普通用词，多指在战争、比赛、竞选或辩论中战胜对手，侧重胜利的暂时性。）

Example:

Napoleon was defeated by the Duke of Wellington at the battle of Waterloo.

拿破仑在滑铁卢战役中被惠灵顿公爵击败。

They defeated the Italian team and reached the final.

他们打败了意大利队，晋身决赛。

He defeated the champion in three sets.

他三盘击败了冠军。