Among the great ancient rivers in China, the southern ones are called jiang1 and he northern ones he2. We are speaking here of your Chinese Volga, Nile, and Mississippi. Jiang1 seems pretty clearly to be related to ancient non-Chinese words for "river" of the languages of what is now South China, and he2 may be the most "native" Chinese word.

But Chinese literate culture has been using these terms somewhat indiscriminately in the many thousands of years since jiang1 was "foreign", and that's why the geographic distribution seems so hazy.

Shui3 and xi1 (qi1) are also common words, but they refer to smaller rivers. And various dialects have sometimes adopted special terms for creeks and brooks - I've heard "port" (kang2 ) and "dike" (pi1 ) used for local bodies of flowing water in Taiwanese, and I'm sure there are others. Kang2 really refers to a deep ditch that leads out to a nearby body of salt water, so that sea fish can sometimes be caught in it. Pi1 seems to refer to a river with a high embankment.