Vertebrates are Chordates but all Chordates are not Vertebrates.

Explanation

i.Presence of notochord is a characteristic feature of all Chordates.
ii.In members of subphylum Urochordata, notochord is present in tail region of larvae and absent in adults.
iii. in case of subphylum Cephalochordata, notochord is present throughout the life of the Animal.
iv.However, members of subphylum Vertebrata, possess a notochord only during embryonic stages of development.
This notochord is replaced by vertebral column in the adult stage of Vertebrates.
Thus, due to the absence of notochord in adult Vertebrates, it is said that all Vertebrates are Chordates, but all Chordates are not Vertebrates.