I couldn't find any official definitions of streams. Stream is sometimes used as a generic term to cover anything from a brook to a river. Other times they are defined by size with no official flow rate or other measurement. By size they go from brook to creek to stream to river.
It is difficult because size varies along the path of a stream. e.g. The headwaters of the North fork of the American River near the Pacific Crest Trail behind the Sugar Bowl SKi Area at Donner Summit is no larger than a brook.
Green Brook and Middle Brook near where I live became raging rivers with heavy rains in the early 70's, again with the remnant of Hurricane Floyd in 1999 and in 2007 causing millions in property damage and several deaths. The Army Corps of Engineers (ACOE) is spending $16 Million on a flood control project to protect the town of Bound Brook.
A blog post at LetsReadClassics says:
Dictionary.com defines them as...
Brook - a small, natural stream of fresh water
Creek - (in the U.S., Canada, and Australia.) a stream smaller than a river
Stream - a body of water flowing in a channel or watercourse, as a river, rivulet, or brook
River - a natural stream of water of fairly large size flowing in a definite course or channel or series of diverging and converging channels
So a brook is smaller than a creek which is smaller than a steam which is smaller than a river. I'm just trying to decide if my grandpa's farm has a creek or a stream or a brook that runs along one side. It must be a creek considering it doesn't look nearly as lovely as the description sounds of the brook that streams by Green Gables.
Difference Between Stream and River
stream at wikipedia.
Fundamentals of the Rosgen Stream Classification System at epa.gov
Glossary: stream related terms at StreamNet.org
Flood Warning Terms: at FloodSafety.com
USGS Water Science Glossary of Terms
last updated 27 July 2011