A stream is one of many words for a small river. Streams are normally found near the edges of river basins, perhaps starting as a spring in a hillside and then tumbling down in a small valley towards the main river.
There is no hard and fast rule about when a stream becomes a river, but a stream would be no more than a few metres wide. When it gets to over 10m or so, it will probably be thought of as a river.
Streams are also called brooks, burns and other regional names.
Streams are too weak to change the landscape much and often make many little waterfalls as they move across hard bands of rock. The video shows you an example.