By that same logic every instrument of every type should sound the same, and you shouldn’t be able to tell a singer from a piano.
Notes only have pitch and duration, pitch is how high or low the sound is, and as long as the sound is hitting that pitch then it’s doing the right note.
But we don’t produce perfect square sound waves, every sound has to ramp up to the desired pitch, stay there and then come down. The irregularities (small ups and downs) on the sound as it does that are called timbre and are what allows us to distinguish different sounds, even if they have the same pitch.
You obviously know every person is different, so it follows that their throats will be different and so will their timbre.
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