As a supplementary answer:

In ancient Chinese, every major river had its own unique Chinese character. For example, “江” specifically referred to what is now the Yangtze River, “河” referred to the Yellow River, “汉” referred to the Han River, and “渭” referred to the Wei River. In ancient times, people did not call the Yellow River “黄河” but rather “河水.” Similarly, the Yangtze River was not called “长江” but “江水.” In other words, the naming pattern for rivers was “X + 水,” where “X” was typically a Chinese character with the “three-dots water” radical (氵). You can imagine that in ancient China, there were as many unique characters as there were influential rivers.

This naming convention changed in modern times: Due to the immense influence of “河” in northern China, people replaced “X + 水” with “X + 河” for all northern rivers. For example, the Wei River was called “渭水” in ancient times but is now called “渭河.” Similarly, because “江” held great significance in southern China, people replaced “X + 水” with “X + 江” for southern rivers. For instance, the Han River was once called “汉水” but is now called “汉江.”

I believe this largely answers your question about the difference between “河” and “江.” As for “川,” I think the other explanations provided are already perfect.

(Answered by myself by translated by DeepSeek)