Notochord is the skeletal rod which lies lengthwise between the central nervous system and the alimentary canal or the gut and the chordates possess it at young stage of development. In adult vertebrates, it is replaced by vertebral column. On the other hand, a nerve cord is a solid strand of nervous tissue, forming part of central nervous system, especially of invertebrates. The main difference between the two is that notochord is a part of skeleton system whereas nerve cord is a part of nervous system.
