An advance directive is a way of delegating responsibility to an agent to carry out specific activities and make specific decisions when a person becomes incompetent and cannot make those decisions themselves. This is usually achieved by durable health care powers of attorney.
Power of attorney is a way of retaining control in yourself while delegating certain responsibilities to an agent, or “attorney in fact.” The powers you delegate can be very broad or very specific, depending on your needs.
If you become incapacitated and do not have a durable power of attorney, then a guardian will need to be appointed to make your decisions for you. The problem with this scenario is that you then lose all control to make your decisions and the court may appoint somebody whom you would not choose.
A living will spells out, specifically, what your desires regarding life-prolonging procedures are if you become unable to make those decisions.
You can know what the best planning for those needs is by visiting an estate planning attorney who has the knowledge and experience to ensure that no matter what happens, your goals will be met.