I asked a pianist to play C. I asked an alto saxophonist to play C. They played different notes.
The piano is pitched to C. The alto saxophone is pitched to Eb.
An orchestra with instruments pitched in different keys provides more opportunities for colour in the orchestration.
So how do we define C? C is the easiest key for any instrument to play in. C# and Cb are the most difficult. The more sharps or flats in the key signature the more difficult the piece is to play.
NB: When the piano is in the key of E (4 sharps) alto saxophone is in the key of C# (seven sharps) so E is not a good key for a piano and alto saxophone duet.
Let's hear this melody played by a variety of instruments.
An absolute identifier of pitch is Concert Pitch. At the instruction to play “Concert C” all instruments play the same sound.