What’s the difference between mambo and salsa?

This depends completely on how each is defined. If we are talking about club style salsa and club style mambo, the only difference is that salsa can be danced on any beat whereas in mambo, the break step is taken on the second beat of the measure. Thus salsa encompasses mambo. In other words, mambo can be thought of as the special case of salsa where the break step is taken on count 2.

If we are talking about salsa and ballroom mambo, the differences are larger. Ballroom training encourages precise and sharp movement with sudden stops and fast changes of direction. In addition, big arm lines are used in ballroom figures. Ballroom figures normally have precise geometries and usually move in linear or lateral directions. In contrast, salsa is more relaxed, more flowing, and the patterns are more circular. Big arm lines are not used in club style salsa dancing.