Types of Drain
The purpose of a French drain is to redirect water away from a property or a wall.
The idea of a French drain is to combat surface flooding and normally redirects the water downhill. In essence it is a ditch which is then filled with gravel and stones then covered with soil. Sometimes it can be constructed using pipes but the intention is the same.
When constructing a French drain, it is important that the water doesn't flow into a neighbour's property. It must redirect to a location where it will do no harm.
A trench drain sounds as though it does exactly the same as a French drain. They are constructed in the same way but in actual fact, the trench drain serves a different purpose.
The Trench drain serves to get rid of surface water, not redirect it. It can be constructed of concrete, fibreglass or plastic.