If a band tunes down to B flat how does the notes I play change? Do I play eveything a half step lo?

Wouldn't you just tune to a B flat? I'm classically trained and have been playing for years and I may be wrong, but I would just tune to a B flat. I wouldn't play the music differently, I would just be tuned differently. However, I may be completely wrong. I played an instrument that mostly only played on B flat and rarely tuned to a different pitch.