What is the difference between:
Ich kämpfe für mein Heimatland.
Ich kämpfe um mein Heimatland.
Ein sinnvolles Beispiel, in dem beides vorkommt:
There is a difference, but it is not easy to explain.
This means that I'm fighting for my home country. This implies that I'm working as a soldier or so for that country.
This means that I'm fighting to save my home country, because it is in danger. A german soldier attacking Poland in WW2 might have said the first, because he was fighting for Germany. But only at the end of the War he could have said the second, because then his home country was endangered.
When the second can be said, the first is usually also right. I.e.