Agricultural drainage was developed to take excess water off farm paddocks. 'Ag pipe' is the flexible, corrugated, slotted poly pipe you see in any hardware store. When someone says they'll 'put in an ag line', they usually mean burying that pipe, sometimes wrapped in a sock filter, to collect water. It may or may not include a proper gravel surround.
A French drain is defined by the gravel-filled trench and the deliberate slope to a discharge point, with the perforated pipe sitting inside the gravel. The gravel is doing real work, it provides storage and a free-draining path. So most well-built French drains use ag pipe, but not every buried ag pipe is a proper French drain.
For a soggy lawn or surface water, a simple ag line in a gravel trench may be enough. For protecting a building's footings, intercepting subsurface water on a sloping block, or anything connecting to council stormwater, you want a properly engineered French drain with the right fall, fabric and a legal discharge, and on the structural and stormwater side, a licensed plumber.