The orkhestra of the Theater of Dionysus in Athens was the circular dancing place of the chorus, with the word built on orkheisthai, to dance. Vitruvius describes Roman adaptations. The sense shift to the musicians' area is early modern, and to the ensemble later still.
The storytelling version notes the quiet demotion: in Athens the dancers owned the word and the musicians accompanied; today the musicians own it and dance is elsewhere. The word's path tracks which art form was paying for the building.
Theater traditionalists like pointing out that calling the pit the orchestra restores nothing: the original orchestra was where the audience-facing ritual happened, so the name marks the spot where meaning used to be made and now sound is.
A word that moved from the dancers to the band to the band itself: is a word a thing, or just a place everyone keeps reassigning?