Why is the word "canal" called 运河 in Chinese?
You got the point. 

"运河" must refer the human-made channels in a large scale, for water conveyance/transportion. That's what "运" emphasize. Usually, it connects big lake/river/ocean or through the peninsula or isthmus.

In the meantime, "渠" just refer all human-made channels. "渠" is more like a superset of "运河"; 

But why we don't just call all channel to 渠? Same reason like the water is a superset of the ocean, but you would never call "the Pacific Ocean" to "the Pacific Water".  

Now you can tell the difference between "运河" and "渠".