I was asked this question in my interview at Oxford. How have these two words been used historically? Have the meanings of these two words been manipulated to suit their user's political ends?
Patriotism represents loyalty and love for the state you are a subject under.
Nationalism represents loyalty to a particular community of people with shared background, I.e your ethnic group.
To many in the world, those two words are synonymous because the default political unit in the world today is the nation-state, in which the state is explicitly built for a certain nation. But this is not always true. For instance, an Ukrainian nationalist who sought independence from the USSR can be said to be both nationalist and unpatriotic simultaneously.