Q:

"unwilling" vs. "refuse"

Suppose Sam is a kind of person who always follows his own will when it comes to taking actions. 
In this case, are the two sentences below identical in meaning? 

Sam is refusing to make it happen. 
Sam is unwilling to make it happen. 

A:

Unwilling doesn't necessarily mean that you didn't do something, but refusal suggests so.  
An example Google gives as part of its definition is "unwilling conscripts". 
Being unwilling to serve in the army could mean you grumble while you're there, whereas refusing to serve in the army implies you'll be thrown in prison.