How does course cloning work?

There are two types of course clones: shallow clone and deep clone.

Types of cloning

Course only ("shallow clone") The course is cloned but the modules are not cloned. Editing the modules will edit the modules in any courses in which they appear.
Course plus modules ("deep clone") The course and the modules are cloned. Editing the modules will only affect this course. 
Course plus modules, replace problems ("deep clone plus") Same as a deep clone, but it also marks all the problems as "needs replacing". 

For more info on how Courses, Modules, and Problems fit together, check out Grok's data model.