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Imagine, the piano is sounded $500 \mathrm{Hz}$ sound and the same frequency is sounded in a violin. We always observe their sounds are different even though they're harmonic.
I think there must be some other parameters that provide the same frequency sounds differently. Why it's sounded differently?
If each instrument only played on exact frequency then you would only hear that one, same note. However, what you hear includes other harmonics whose generation depends on the shape and other characteristics of the instrument. If you had a way of analyzing the frequency spectrum of your instruments, you could see directly the differences betweeen them. There's an example for a violin in this answer.
