What is the difference between chordates and vertebrates?

Chordates have a notochord, dorsally located nerve. Vertebrates have a vertebrae or a back bone. All vertebrates are chordates, but not all chordates are vertebrates.

Essentially there is no difference as vertebrates are chordates. Chordates are animals which possess, or at some point in their life cycle did possess a notochord. A notochord is a hollow nerve chord which ends in a brain. Other chordates include the Cephalochordates (lancelets) and Urochordates (tunicates).