Most of the great classic Broadway musicals are musicalized adaptations from other mediums (books, plays, comic strips, etc). The adaptation to the musical format makes it something new.
Original musicals obviously draw this distinction based on their “origins” hence the root word. If the origins are another media, then it’s not original. If a musical is a brand new story with brand new music, it’s “original”.
A show can be nominated for Best Musical Tony regardless of its origin, as long as it is new to Broadway. So it can be an original story, an adapted story, and can have new music or adapted music (jukebox musicals, etc). Obviously, only new music qualifies for best music and lyric Tony nominations.