The reason why the same note sounds different on different instruments, even when they are tuned to the same pitch, is due to a combination of factors: the instrument's physical characteristics, the materials used, the construction, and the playing technique.
Tone color/timbre: Each instrument has its unique set of overtones and harmonics, which contribute to its tone color or timbre. These additional frequencies give instruments their distinctive sound. For example, a note played on a violin will sound different from the same note played on a trumpet due to variations in the harmonic content.
Resonance and soundboard: Instruments have different resonant properties and mechanisms for producing sound. The shape, size, and materials of an instrument affect how it resonates and amplifies specific frequencies. For instance, the body of a guitar or a piano soundboard influences the quality and richness of the sound produced.
Playing technique: The way an instrument is played also affects the sound produced. Factors such as the bowing technique on a violin, embouchure on a wind instrument, or finger placement on a guitar can influence the tone and characteristics of the note played.
Harmonic series and intonation: Instruments differ in their ability to accurately produce the harmonic series. Instruments like brass or woodwind instruments have a set of partials that may deviate from the ideal harmonic series, leading to variations in intonation and tonal characteristics.
Attack and decay: The initial attack and subsequent decay of a note can vary between instruments. This can be influenced by factors such as the instrument's attack time, envelope shaping, or the speed at which the sound dissipates.
All these factors contribute to the unique sound of each instrument, even when playing the same note at the same pitch. The combination of physical characteristics, materials, construction, and playing techniques results in subtle differences in timbre, resonance, and overall sound quality.