A good live performance is intentionally not 100% the same as in the studio, but there can and should be variations. A refrain repeated another time, some improvisation here. Playing with the tempo there. It takes a good band, who know each other intimately, to make that work, though. (a good DJ can also do this with electronic music)

A recorded studio version, I can also listen to at home. But a full band performing in this very moment is a different experience to me.