Geotextiles are typically porous, used in filtering, separation, or draining applications, while geomembranes are meant to halt the flow of liquid or gasses, and don't allow the fluid to pass through. You will most typically find geomembranes being used to contain, rather than filter or drain.
While geotextiles are made out of blends of synthetic fibers, geomembranes are instead manufactured through woven blends of impermeable polymers.
