The main difference between running a country and a business is that quite possibly the common sense assumptions that work at one scale don't hold at the other.
Economics is often counter-intuitive - especially at a global scale. People extrapolate their intuitions from household economics to national level and beyond. There's no guarantee that any of our assumptions are still valid when you consider the entire world as one closed system.
The main difference between running a country and a business, is values and also means. Countries value certain qualitative indicators more than a typical business would (quality of life, crime, safety, etc...), and countries have more means to balance the books (things like printing money, ownership of resources, etc...).
Talking about money at small-business scale is more about simplifying the concepts, but to a certain degree, it applies.