Here's how they differ:
* Coarse refers to something rough in texture, like coarse sandpaper or coarse fabric.
* Course can refer to a path or route, a sequence of lessons, or a part of a meal.
Here are some examples:
* Coarse - "The fabric felt coarse against my skin."
* Course - "We took a course on how to use the software."
* Course - "We're having a three-course meal."
* Course - "The ship took a new course to avoid the storm."