Coarse means rough. Course is a class, a path, or of course. Coarse sand. A history course. Diction as a set is in word choice.
Texture versus path
If you can swap in rough, use coarse. If you can swap in class or route, use course. Of coarse is the usual miss.
Council versus counsel is another look-alike pair, in council versus counsel. Accept versus except is in accept versus except. Grammar overall is in ACT grammar rules.
The bottom line
Rough: coarse. Class or path: course.
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