Well, by Field Hockey I think you mean hockey games that are done on the ground like field hockey, street hockey,ect. It is called Ice Hockey. *Field hockey and ice hockey are completely different rulebases. As the first answer pretty much describes, it is simply called "field hockey on ice", like it is called "field hockey on grass", "on turf", "on concrete", etc.
Ice hockey is played on ice, while field hockey is played on a grass surface, the rules in field hockey are kinder than ice hockey, and the sticks vary between versions.
ice hockey is a rink and field hockey is just a field
Ice Hockey is Hockey played on ice; as compared to Field Hockey which is played on grass.
roller hockey ice hockey and field hockey
Hockey was historically not played on ice until around the invention of modern ice hockey. This was well after the creation of modern field hockey, which itself derived from earlier variations. In short: field hockey was first.
Field hockey is a field sport, but both indoor and ice hockey are rink sports.
Field Hockey or Lacrosse
Field hockey variants have been played for thousands of years; ice hockey was only begun in the 18th century.
On the field (best kind), the ice, gym floor, or pavement.
No, only ice hockey and field hockey are.