A power of attorney is authorisation to act on another person’s behalf and in their name in a legal or business matter. The person granting the power of attorney is known as the grantor and the person authorised to act is the agent or attorney-in-fact. The power granted may be very wide in scope and may include the power to sign documents on behalf of the grantor, deal with their financial affairs and property, etc.
A proxy commonly refers only to authorisation to vote on another’s behalf and is therefore more limited in scope than a power of attorney. For example, a shareholder entitled to attend and vote at a company meeting may appoint a proxy to attend and vote in their place or a British student backpacking around the world may appoint his or her mother to vote in a general election on his or her behalf (note that a proxy is also the person to whom authorisation is granted).