Nice write up by Marc about ruby extend and include. He succinctly explains what each of the methods do, however I think his explanation is for a ruby programmer, not a C# programmer trying to learn more about ruby. Upon further research I found another post that made it quite clear for me.

The extend method will mix a module’s methods at the class level. The method defined in the Math module can be used as a class/static method.

The include method will mix a module’s methods at the instance level, meaning that the methods will become instance methods.

It is much easier for me to relate that to what I am familiar with in C#.