I believe the "calving" term continues to be used as the bergs get smaller becoming "bergie bits" when they drop below about 5m high of visible ice and later "growlers" when their height drops below 1m.
I believe an ice floe is a predominantly flat piece of ice which comes from floating pack ice, i.e. usually from frozen sea water. Bergs calve from freshwater ice i.e. glaciers. If brash ice and/or growlers are kept together by wind and/or current and the water around them refreezes then you can have a floe which is part fresh/ part salt water.