There are two words here, though their spellings are easily confused. The word for a rope or thick string is spelled cord, while the musical term describing the simultaneous combination of notes is spelled chord. This may seem quite straightforward and uncontroversial, but it’s interesting to observe that this distribution of the two spellings is unetymological. The word we now spell cord is a borrowing of the French word corde, ‘string, rope’, which itself is derived from the Latin chorda. It is first recorded in English in the 15th century in the spelling cord; however, in the 16th century it was respelled chord to reflect its Latin origins. This spelling remained common in the 17th and 18th centuries; it has survived into modern usage in certain specialised senses, such as ‘that touched a chord’, and in the name of the musical instrument harpsichord.
Despite its spelling, the musical term chord is unrelated to Latin chorda; it derives from accord in the sense ‘bring into harmony’.The musical term first appeared in English in the 15th century, when it was spelled corde; this word survives in the spelling of accordion. In the 16th century it was confused with the word corde, ‘string, rope’, and subjected to the same change in spelling, giving us the word chord. So, while the spelling of these two words might appear straightforward, their histories show that the spellings are, etymologically-speaking, the wrong way round. Chord should refer to the rope, and the musical term should be cord. While this confusing history may appear to have been straightened out in today’s usage, it has left some vestiges of uncertainty. Should it be ‘vocal chords’ or ‘vocal cords’ for instance? The usual spelling today is vocal cords, but it’s common to find vocal chord. This is frequently stigmatised as a folk-etymological spelling, implying confusion with the musical sense of chord, but it’s actually a genuine survivor of the older spelling, first recorded in the 18th century.