Nationalism, in current usage, tends to mean jingoism. The difference between that and patriotism could be described as the same as the difference between love and obsession.
Modern meanings of nationalism are synonymous with jingoism. It was once in the definition list on Wiktionary, but was conveniently removed late last year.
and if you follow that link, it refers to the 3rd definition of patriotism:
"The desire to compete with other nations; nationalism."
Patriotism is a better fit for this use, as there's the first definition:
"Love of one's country; devotion to the welfare of one's compatriots; passion which inspires one to serve one's country."
Generally, if we're not using literal dictionary definitions, in a political context, nationalism is overpowering patriotism where you want your country to be better than others at all costs. Patriotism is a love for you country and your people.
[0] https://en.m.wiktionary.org/wiki/nationalism