the same note doesn’t sound exactly the same if it’s played by a guitar, a piano, a violin or a human singer. The reason is that each instrument has its own timbre for a given note.
For each instrument, the sound produced is a multitude of frequencies that sounds like a given note (the scientific term for a musical note is pitch). This sound has a fundamental frequency (the lowest frequency) and multiple overtones (any frequency higher than the fundamental).
Most instruments produce (close to) harmonic sounds. For those instruments, the overtones are multiples of the fundamental frequency called harmonics. For example the composition of pure tones A2 (fundamental), A4 and A6 is harmonic whereas the composition of pure tones A2, B3, F5 is inharmonic.
Many percussion instruments (like cymbals or drums) create inharmonic sounds.
Note: The pitch (the musical note perceived) might not be present in the sound played by an instrument. For example, if an instrument plays a sound with pure tones A4, A6 and A8, Human brain will interpret the resulting sound has an A2 note. This note/pitch will be an A2 whereas the lowest frequency in the sound is A4 (this fact is called the missing fundamental).