What is the difference between “libertarian” and “compatibilistic” freedom?

Question: I often hear philosophers and theologians talk about “libertarian” and “compatibilistic” freedom. What do these terms mean? 

Answer: A person who holds to “libertarian” freedom believes that an agent (human or angelic) is truly free and morally responsible for their choices only if it resides in an agent’s power to determine his or her own choices.  Their decisions, in other words, can’t be completely determined by causes outside of themselves. Given any choice an agent makes, a libertarian holds that the agent must have had the power to choose differently if their choice is to be truly free and morally responsible. This is sometimes called “the power of contrary choice.” It is also sometimes referred to as “incompatibilistic freedom,” since the belief is that free will is incompatible with determinism.   

By contrast, a person who holds to “compatibilistic” freedom believes that an agent (human or angelic) can be said to be truly free and morally responsible for their choices if there is no obstacle to their choosing what they want, even though what they want is completely determined by causes outside of themselves and even though their choices are completely determined by what they want.  In other words, compatibilists believe that free will is compatible with determinism.