All vertebrates are chordates but not all chordates are vertebrates. Why?
Phylum Chordata includes protochordates (urochordates and cephalochordates) and vertebrates. Protochordates have a notochord (at least at some stage of their life) but lack a vertebral column. Vertebrates possess notochord during the embryonic period. The notochord is replaced by a vertebral column in the adult. So, all vertebrates are chordates (have a notochord). Protochordates are not vertebrates (lack a vertebral column). Hence, not all chordates are vertebrates.