Dunno about minuet/scherzo and trio. The trio is a contrasting section that's generally a lot longer than a typical middle 8. It's often taken at a slightly slower tempo than the minuet/scherzo. Occasionally there's more than one trio, such as in the third movement of the New World Symphony and in a minuet of Mozart's Gran Partita and in his Clarinet Quintet. Quite often the trio is played more than once (Beethoven 7, Beethoven 9 and many more).

In all these cases the trio, the "instrumental break" or the middle 8 are there to provide contrast, an important element in any genre of music. In classical music, other devices may be theme and variations, rondo and sonata form (with contrasting first and second subjects and development and recapitulation sections). The sentiment for providing contrast within a whole that still manages to hold together is the same in all genres, though the devices used are legion.