Almost but not quite. In practical terms:
1. An Advance Health Directive (AHD) overrides a Power of Attorney (PoA);
2. A PoA overrides a Statutory Health Attorney (as so does an AHD...) ;
3. All of the above is based on the care giver being aware of their existence. If they don't know about the PoA or AHD, they're not going to wait around looking for one.
4. An AHD can cover issues which the PoA cannot. From the health angle, these are things like tissue donation and termination of pregnancy.
Otherwise:
- a PoA is you giving someone else the power to make the decision (subject to your specific instructions); and
- an AHD is your specific wishes on particular issues stated in writing. For example, 'if I am in a coma I do want hydration but I do not want food or antibiotics' - it's set out differently, but that is the gist of it.