Chozeq yad is the institution of property rights; shemitat yad is the divestment of property rights.
Chozeq yad signifies claims of ownership between God and the Children of Israel. By God claiming to own the Children of Israel He is making them belong to Him closer than the other peoples in the world, who are less His own than are the people of Israel.
Shemitat yad, in contrast, signifies those who resemble each other so much that property exclusions do not make sense. Those who merit shemitat yad, for example, are members of the same family.