All chordates are vertebrates

Chordates include the vertebrates, or animals with backbones. However, not all chordates are vertebrates. Some chordates, such as the cephalochordates lack a spinal cord, and hence are not vertebrates.

The term chordate does not refer to the spinal cord, but rather the notocord. This is a stiff but flexible rod that runs the length of an animal at some stage of its life, whether embryonic, or adult. Other essential chordate features include gills, tails, and a nerve cord.

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