Essentially, there is very little difference between a stream and a river. Both involve a flowing body of water, usually freshwater. Streams are small flowing bodies of water that find a place in caverns, crevices or relatively flat areas. Rivers are larger streams that move massive amounts of water. River typically have stronger currents and are found in places with higher slopes.
Both rivers and streams have three different types, all of which describe the shape and formation of the water. The three types are straight, meandering and braided. Straight streams and rivers simply flow in a straight manner, often coming from melted ice at high elevations. Meandering rivers and streams follow the natural lay of the land, and they weave in between rocks and other landmarks. Braided streams and rivers have an "S" shape, and they fold back on themselves, which is why these bodies of water sometimes form tributaries or ponds.
Streams and rivers play a huge role in shaping land over time. The Grand Canyon, for example, was formed by a river that gradually eroded the rocks to form the massive gap that is present today. Streams and rivers carry soil and erode rock in two ways. The first involves what is called a suspended load, in which a river carries larger particles in its current downstream. The second involves what is called a dissolved load, which occurs when a stream or river breaks down microscopic particles that dissolve in the water and move downstream. Both of these methods are the means by which rivers and streams form different landforms.
In general, all rivers start out as streams. Streams, which may come from melting ice caps on mountains, hail or sleet, rainfall or melting glaciers, form at very high elevations. These streams, with very weak currents, trickle down to lower elevations. As various streams trickle down to a location, they may meet other streams and form bigger streams. Once enough streams have joined to form a larger flowing body of water, they become a river, which eventually empties into an ocean.