A
creek is the normal word we use in many rural US regions, perhaps especially toward the south, for a small, narrow, flowing body of water, much smaller than a river, between often somewhat steep banks. Usually very shallow, often somewhat rocky, but can contain minnows and sometimes small fish. A creek can run dry in a very hot summer, but a dry creek bed (in the US southwest) that never has water except after a heavy rain is a
gully or an
arroyo.
A
stream I think of as flatter, stiller, and somewhat wider and deeper than a creek, but still much smaller than a river, with a more consistent flow of water and more reliable stocks of fish, usually in more northern regions with more rain. A
trout stream is typical in rainy, hilly places like Scotland or the US Pacific northwest, with fast-flowing water but enough depth for larger fish. A
mountain stream is another fairly fixed collocation, in contrast to a creek which is usually in a low-lying area. But a really low coastal area, with green wetlands that flood, could have streams in among the marshes; anything with completely flat banks at the same flat level could also be a stream.
The word
brook isn't generally used in conversational AE, at least in my part of the country, so to us it sounds literary or poetic. Tennyson or someone wrote about a 'babbling brook,' and that phrase has become a cliché. It does still appear in names intended to evoke an attractive outdoor setting, like 'Brookdale,' 'Brookside,' etc., and 'Brookshire' is a last name.
https://rpo.library.utoronto.ca/poems/brookhttps://rpo.library.utoronto.ca/poems/elegy-w... (l. 104)
Other speakers may have other associations.
