They are not really synonymous. If you go to an art gallery for example you will generally see "exhibitions" (e.g works of art by a particular artist or on a particular theme). "If you go to a large city where there are objects from many diverse (sometimes international) sources on show attracting a wide and diverse audience, this might be an "exposition". In earlier times this might have been called "Great Exhibition". The word "exposition" is more usually used when someone is giving a structured "explanation" - perhaps in an academic or business context etc. There is also sometimes a confusion because the word exposition in French is usually translated as exhibition in English. These 2 words (in this context) are generally considered to be "false friends". Hope that is of some use...

They are interchangeable, however, "exposition" is commonly used to describe a larger exhibition.