"The other way around" is an expression, meaning something is positioned opposite of where it should be or where it was. It is "the wrong way around." Example: The dog meowed and the cat barked. It should be "the other way around." The dog barked and the cat meowed.

other way round means contrarywise/inversely... this sentence implies that the speaker not quite agrees to what he was said and he thinks that it will work just the opposite way. A- you know what? many men, many minds. B- i think its just the other way round; many minds, many men.