I tend to think of creeks as the smallest of the three, with streams being in the middle, and rivers being the largest. A river is nothing more than surface water finding its way over land from a higher altitude to a lower altitude, all due to gravity. When rain falls on the land, it either seeps into the ground or becomes runoff , which flows downhill into rivers and lakes, on its journey towards the seas. Flowing water finds its way downhill initially as small creeks. As small creeks flow downhill they merge to form larger streams and rivers.
Rivers eventually end up flowing into the oceans.
If water flows to a place that is surrounded by higher land on all sides, a lake will form. If man has built a dam to hinder a river's flow, the lake that forms is a reservoir. The water in a river doesn't all come from surface runoff. Rain falling on the land also seeps into the earth to form ground water . At a certain depth below the land surface, called the water table , the ground becomes saturated with water.