This is the right way to put it
Nation: a country considered as a group of people with the same language, culture and history, who live in a particular area under one government.
A nationalist will thus fight for a state/goverment that is a result of, and consists of common culture, language, history etc.
By this he tries to create/maintain the so-called nation-state. Basques, Scots, Ukrainians, Sudeten Germans, Croats among lots of others.
Partisan: a person who strongly supports a particular leader, group or idea.
Communists, anarchists, fascists, conservatives; those fighting for a certain way of governing, an idea.
Patriot: a person who loves his country and who is ready to defend it against an enemy.
A patriot fights for a community or his state, ussaly across ideas and nationalities. Americans, Frenchmen, Spaniards, Britons etc.
These three terms are, of course, abstract and overlapping. An "insurgency" may include all three concepts. Nevertheless, I believe that the most dominant identity of those who rebel will classify the type of insurgency. Soviets is like both patriots and partisans, however, most classify them as a partisans. A Nazi German is both a nationalist and a partisan, however, most classify him as a nationalist.