I think players that train together or learn from each other may develop similar playing styles but that has more to do with them playing together as a group as opposed to where they were born. Yes, there are "schools of thought/chess" that refer to the countries or nationalities of the first/best players to use those styles but it is my opinion that those styles could have developed elsewhere and aren't country specific.
Do different nationalities have different styles?
I don't know but my style seems particularly effective against players from France. Maybe just a coincidence...
IT IS A FACT THAT THERE ARE MORE GRAND MASTERS FROM RUSSIA==
Iceland has more GMs per capita than any country .
Some ideas in chess are particularely Russian, such as the Russian exchange sac, the Siberian trap (I think) and the Dutch defence, especially the Leningrad. (But don't forget the Ilyin-Zhenevsky.)
That being said, I never noticed the nationality in itself was much of a factor. Karpov was one of the most positional players of all time. I don't have to tell you there have also been tactical monsters from Russia.
Nakamura started out as an intuitive player, who learnt by doing. (Changing a bit now) Fischer on the other hand was known for his home preparation.
I usually need to concentrate more when playing an indian player at my level than any other nationality in the same range. Ever so often I'm surprised by a rather vivid attack seemingly coming out of nowhere if I fail to pay close attention.
Not sure if this is my imagination playing tricks on me, but the tendency is quite clear; indians are sharp! :)
Do you think that different players from different countries have a certain stereotypical style of play? Like aggressive or positional, not "Russians are stereostypically good"