A French drain is sub-surface with a perforated pipe surrounded by gravel. As water hits the gravel it travels to the pipe which redirects water away from an area.
Surface drains are catch basins that capture the water at low points in the yard and divert that water using a solid pipe.
While French drains can be very effective it is much more common to need a surface drain. And please be aware using a perforated pipe with surface drain or gutter down spout can create problems as that pipe with only inject the water right back into the soil.
