Alright, here’s one for you.
What’s the difference between a stream, a brook, and a creek? (I could include rivulet but that’s probably a different category altogether.)
The size is the difference…don’t forget crick, too.
Not a whole lot.
Around here, a stream has to have water in it to be a stream. A ‘stream’ could be argued to be the water rather than the thing it runs through.
A creek, or crick, can be dry.
A brook is stream that makes noise, or a girl I knew in school.
I’ve never heard anyone call anything a rivulet.
I have a crick in my back yard, that runs into a stream a mile away. A few miles further there’s a very nice brook that cuts into the bedrock while going down the bluff, creating a waterfall I like to photograph. I don’t have any shots of the waterfall online, for some reason.
Are there cricks anywhere except in southern Ohio? There aren’t any in Mississippi, Georgia, Tennessee, Florida, etc. 
Actually, that was a joke on my part…a rivulet is a tiny stream, such as that water trail coming down the window of your car or a little stream coming down your driveway after a hard rain.
I got to wondering about rivulet which is clearly a diminutive, but a diminutive of what word? A rivule? So I looked it up. The diminutive appears to have been taken directly into English, with a little spelling change, from Latin leaving the original, non-diminutive (what’s the word for that?) behind. The root is rivulus which is the diminutive of rivus meaning, as everyone agrees, stream.
Crick is the variant of creek used throughout Appalachia and in those areas to the west settled by emigrants from Appalachia.
Today in the U.S., the words stream, brook, and creek are basically interchangeable, although brook is probably the rarest of the three words and may have poetic associations not common to the other two. (I do not know any place in the U.S. where brook is the familiar word for small flowing bodies of water, although it does show up in a few place names.)
Creek originally meant the opening of a small bay into the sea or, by extension, the opening of one small stream into a larger stream or river. When North America was being explored, numerous examples of such creeks were noted by those who first surveyed the coasts and larger rivers. As the land was settled, the people exploring the extent of these creeks discovered that they were, in fact, streams. Since they were more familiar with the word creek to name the body of water along which they lived and they were now separated from the source of the English terminology, they began to apply the word creek to any stream. (This usage for creek, along with the word bluff to mean a high embankment, are among the earliest examples of the separation of American from British English.) I don’t know whether or not the English (following the inundation of U.S. soldiers in two wars and millions of tourists and hundreds of television shows) have begun to use creek to mean stream.
Rivulet is simply a very small, rather fast stream of water. I have encountered it most frequently in references to “rivulets of sweat” pouring off one’s face or “rivulets of melting snow” runoff. I don’t know whether or not it is commonly used to describe a constant flow of water anywhere.
Nothing I have described precludes other usages in Canada, Britain, Australia, or other English-speaking locales.