The first is a "living will." Although the name is similar to a living trust, it does something very different.
A living will lets your physician know the kind of life support treatment you want in case of terminal illness or injury. It is very limited -- it only applies to life support in terminal situations -- and in some states, your physician is under no legal obligation to follow it. So, a living will doesn't give you a lot of control.
A "health care power of attorney" is better. It lets you give legal authority to another person (like your spouse or adult child) to make ANY health care decision for you -- including the use of life support -- if you become unable to do so yourself. This document is much broader than a living will, and it can be legally enforced.
If you want an estate plan that will give you all this control -- both financially and medically -- here's what you need to do.