It is the responsibility of the patriot to protect his country from its government.
– Thomas Paine
It seems that nationalism may indeed be a form of patriotism, but not in its purest or proper form. As indicated by the quote, a patriot does not equate his country with his government. Instead the country is more of an intangible entity that embodies the people's ideals, morals, thoughts and principles. A patriot would consider the interests of his country to be the same as the interests of the people and their morals.
On the other hand, a nationalist would equate his country with his government. An American nationalist would say that all the greatness of America comes from its government and is likely to be intolerant of critiques of the it. Whereas, a patriot would be most moved by a statement against his people and/or their beliefs.
A modern example of the difference between a patriot and a nationalist would be regarding views on the U.S.'s invasion of Iraq. Nationalists would support the idea because they will want to agree with the government and support it in its ideas. Patriots are more likely to oppose the ideas because they feel it violates principles that the majority of American citizens believe in (like sovereignty, freedom, liberty and responsibility).