Well, there are a lot of differences when it comes to individuals and countries. Individuals deal with economics based on microeconomics, and countries deal with it on the base of macroeconomics (the big picture).
However, they both must deal with things like:
- Inflation
- External costs
- Acquiring/providing public goods
- Dealing with economic welfare
- Utilities
- Living standards
- Trading and interacting with neighbors (locally or internationally)
- Improving the environment