These terms are often used today in ways that are similar to one another, but there is a difference that we can identify. The basic difference is that nationalism is a much more aggressive attitude.
We can define patriotism as the feeling of loyalty to one's country and the feeling that one's country is better than other countries. However, we must also add to that definition. Patriotism does not seek to impose its ways on other countries. This is the major difference between it and nationalism. Nationalism, too, believes in the superiority of a given people. However, it translates that belief into a belief that those superior people have the right to conquer other countries and peoples.
Therefore, nationalism and patriotism are similar, but the one is much more aggressive than the other.