I always figured nationalism was the mindless "usa usa usa" chant, which, you know sometimes that's fine, hockey games or whatever. It's okay to feel good about your country, just don't take it as a serious political theory
Patriotism is actually giving a shit about your country and doing something about it - joining the military, voting, speaking up, civil disobedience, actually trying to make our country better. Sometimes you gotta break some nationalistic eggs to make patriotic pancakes. (yes I know the saying is omelette but patriotic pancake just sounds better)
Leading example would be mlk jr. Nationalistic? Hell no. Patriotic? He has his own holiday now, you tell me.