Although these two words are termed the same, they do have their differences in their actual meanings. A politician is someone who attempts to gain personal advantages, most likely by scheming or maneuvering. Also, a politician belongs to a political party, and most likely is far more interested in the betterment of their party then that of the nation in whole (http://www.unique-design.net/library/word/politic.html).
On the other hand, a statesman is a person who, even if they do belong to a political party, can put their party obligations aside and do what is in the best interest of the country. In a long-term perspective, statesmen who put the needs of their country before their personal or party needs will better benefit out nation (http://www.bartleby.com/61/71/S0717100.html).
George Washington: I would label George Washington as a statesman because during his time of leadership of our country, there were no political parties present. Also, Washington made his decisions in regard to what would best benefit our country in short and long term perspectives. George Washington also made the decision of limiting a president's power to where he could not have such authority as that of a dictator or such other type of leader.
Alexander Hamilton: I would also call Alexander Hamilton a statesman. Hamilton's six part plan to relieve the United States of its foreign and domestic debts was indeed for the good of the country. Also,...