Both proxy and Power of Attorney entitles the holder to act on behalf of another person. However, they are used differently, although they are sometimes used interchangeably.
A Power of Attorney is a legal instrument authorizing one to act in the place and in the stead of another person in a general sense, which is called General Power of Attorney, however, there are several different types of Powers of Attorney dedicated for certain purpooses, such as a Financial POA or Special POA.The proxy is a document typically authorising another person to cast a vote in the shareholder's name.
There is another use of proxy, namely a health care proxy, which is a document through which you legally appoint another individual to speak and make decisions on your behalf in the event that you get incapacitated.