The New Jersey "Deer Head" variety is so-named because of the unusual shape of the horse's head. The snout has an angular top edge and the jawline curves upward at the neck -- both of which are uncharacteristic of a horse's features. The "Deer Head" appelation is questionable since deer do not have manes, but it recognizes the unusual appearance of this variety.
Two die varieties comprise the entire "Deer Head" category: Maris 34-J and Maris 34-V. The 34-J is relatively common, while the 34-V is relatively scarce.
High grade examples are very elusive. Anything above Very Fine is a real find. No Mint State examples are known.