[GraemeJ]

Re: I'm not sure, but it seems to me that identical tunes in a particular key would be the same regardless of which book they were in, a key is only the name for a particular series of notes after all is said a done.

Actually the songs would not be identicial. Each song for the Bb instrument should be written a full step (two half steps) lower than the same song for the C instrument.

[So, for example, if the Sax player plays a Bb, he will be playing the same note as a "C" on the piano.]

That's one way of looking at it, but the relative pitch between the notes is the same so, in that sense, the tunes are indeed 'identical'.