The deep water can cause both a ditch or a gully. The formation of a gully or a ditch is dependent on the topography of the land and the speed of the flowing water.
Often times a deep ditch carved over time by running water is called a trench. It can also be called a ditch.
Canyon
The difference between a gully and a ditch is that a gully is a deep ditch. Also a ditch is a lower grade in the earth where water collects and pools.
The men dug a deep ditch to lay pipes for the new septic tank. I fell in the ditch, but luckily it was dry.
It varies, but it is usually 50 feet deep in most places.
A long, narrow deep ditch.
A canion.
arroyo - deep gully cut by an intermittent stream.
fissure, volcano, ditch, valley.
A trench is a deep ditch sometimes surrounding a fortification.
Another word for a deep ditch that is dug around a castle is a moat. You could call it a trench, or you could fill it full of water and call it a moat.