A front garden, or frontyard in America, is usually an ornamental space rather than a social space. In England, Hollandand North France it is often treated as a flower garden bounded by a fence. In America it is more common to have an unfenced front yard with grass near the public road and foundation planting near the house - there is a feeling that putting up a fence is an act of unfriendliness to the neighbours. A backyard is more of a place for family use. It may well be unfenced but is likely to have a degree of privacy.
English front garden - in London
English front garden with view through to back garden
American frontyard with foundation planting
American front yard with foundation planting.