The phylum Chordata is divided into 3 subphyla i.e., Urochordata or Tunicata, Cephalochordata, and Vertebrata. So, we can clearly say that all vertebrates are chordates, but all chordates are not vertebrates.
Thus, the Assertion is correct.
It is true that in adult vertebrates, the notochord is replaced by the vertebral column. This statement is telling us why all chordates are not vertebrates, but it is not telling us why other chordates are considered as chordates only but not as vertebrates.
Thus, the Reason is correct, but it is not an exact or complete explanation for the Assertion.