What's the difference between "HAND OFF" and "HAND OVER"?
In the U.S. Air Traffic Controllers initiate handoffs and receive handoffs.  Perhaps the term "hand over" is general term applied to the process of making/receiving a "handoff."  

Here is the definition of "Handoff" from the Pilot/Controller's Glossary in the FAA JO Order 7110.65W, Air traffic Controller's handbook:


  HANDOFF
  −
    An  action  taken  to  transfer  the  radar
  identification  of  an  aircraft  from  one  controller  to
  another  if  the  aircraft  will  enter  the  receiving
  controller’s airspace 
  and radio communications with
  the aircraft will be transferred.


I am unable to find the term "Hand Over" in the 7110.65W.