Phylum chordates includes two subphyla
(i) Protochordates (urochordates and cephalochordates) or Acraniata
(ii) Vertebrates or Craniata
All chordates have notochord present in some stage of life. In vertebrates the notochord is present in the embryonic stage. This is replaced by a vertebral column during the adult stages.
This confirms that all vertebrates are chordates but all chordates are not vertebrates, they may be protochordate.