POA allows you to sign for a person according to their wishes. They must be competent to appoint you. If they DON'T want to go to a nursing home, you can't send them to one. A GUARDIAN is appointed by the court for an incompetent person. You CAN sign them into a nursing home and you MUST report to the court annually to account for all their finances.
By well-being I meant all the aspects of their lives. POAs, of course, will do things that are in the best interest of the person. A POA becomes an agent for the person.
They are two very different things. A POA has authority to act as an agent for a person, while a guardian is legally responsible for a person. A good way to understand it is thinking how parents are legal guardians of their children. If you have guardianship of a person, you are responsible for their well-being. If you have POA, on the other hand, you just have authority to do certain things for the person when he/she can't do them. It is similar to an attorney that represents a client, but is not responsible for their well-being.
A GUARDIAN is appointed by the court for an incompetent person. You CAN sign them into a nursing home and you MUST report to the court annually to account for all their finances.