A cord can be many things. It can be a string or rope, an electrical cable, or a measure of wood equal to 128 cubic feet. It can also be a ribbed fabric (like corduroy), or one of several types of cords found within the bodies of animals (the spinal cord, the umbilical cord, and the vocal cords).
A chord is typically a musical term denoting any combination of two or more pitches played at the same time. It can sometimes refer to an emotion as well.