Someone who's nationalistic believes their country is better than any other country. Flying the U.S. flag in your yard makes you patriotic, but getting an enormous tattoo of it is a clue that you're nationalistic.
Nationalism is an extreme form of patriotism in which people aren't just proud of their country or culture, but feel strongly that it's superior to others. Believing this makes someone nationalistic. Both words stem from nationalist, once a synonym for patriot, from an obsolete meaning of national, meaning "patriotic." The Latin root is nationem, "origin, species, or tribe."