The difference likely lies in connotation. Nationalism is almost exclusively political in nature, whereas patriotism is often not. In effect, nationalism is the politicization of patriotism. It does not necessarily mean a belief in national supremacy, just as racism and racial supremacy are subtly different.
Nationalism in this day and age is simply the rejection of globalism, and on that, I firmly put myself in the nationalist camp.
That is also a good way of looking at the question.