The Rio Grande river is an example of a physical boundary between two countries since it is a landform. Physical boundaries are very diverse and can include oceans, seas, mountains, rivers, and lakes, just to name a few of the many landforms that can make a physical boundary.
A cultural, geometric or religious boundary could perhaps be visible with the right type of map, but a river does not tell us anything about the religious makeup of a certain area, nor does it reflect the cultural of the inhabitants.