The two words may be used interchangeably. However, there are slight differences in meaning between the two and it mostly has to do with the type of event being presented. In the United States and elsewhere, a stadium refers to a large, usually outdoor structure consisting of a playing field or stage partially or completely enclosed by tiers of seats where spectators may sit and watch. Hence, a stadium is usually designed for outdoor sports such as association football (soccer), American football, cricket, baseball, and stock car racing. An arena, on the other hand, is usually designed for indoor sports such as Basketball, Ice Hockey, volleyball, Wrestling, and rodeo. Both a stadium and an arena are almost identical in design and construction except that a stadium is usually for outdoor sports and an arena is usually for indoor sports.
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The main difference between a stadium and an arena is acoustics. The preferred venue for a musical event such as a concert would be an arena.