What's the difference between 探検 and 遠征?
Is this the same as the English difference between exploration and expedition? 探検 (exploration) is a journey to an unknown place to learn about it while an expedition 遠征 is a journey to a known place organized by someone important with the purpose of learning more about the place or with some other purpose

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Answer

「探検」　is an exploration but basically something you venture.

「遠征」　basically means to go（征）far（遠）

In a dictionary for 「遠征」:
A) An expedition to chastise distant enemies.（十字軍の大遠征）
B) To go far away for a game, a tour, climbing and an exploration.（サッカーの遠征試合。バンドの遠征ライブ。ヒマラヤへ遠征する）

「探検」 and 「遠征」 is nouns. By adding 「する」 following the nouns you can get verb forms: 「探検する」「遠征する」