There are enormous differences. A country is not at all as easy as running a club. In a club, it's just a few people; in a country, there are millions, each doing many things, from good to neutral to very bad. I don't think it's easy to make a country function properly, especially if the people who live in that country don't cooperate to do things right.

How would I know, I have never managed a country team or a club. :
I think there is not much difference, you train and manage team in the same manner.