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I think you might be missing an important part of GDP per capita, and be asking a slightly confusing set of questions as a result.
Per capita means per person. "GDP" and "GDP per capita" are each very different numbers.
GDP - tries to measure the total economic output of the country. It might be what you want to use to compare the raw economic might of two economies.
GDP per capita - This is just scaled by the population. You might use it to see if a small country like Monaco is punching above its weight.
Median GDP per capita - This third measure is what you might what to use to see how the average citizen in a country is doing. Ideally you'd want to also control for cost of living, but generally a bigger number here means higher quality of life for its citizens, even if the cost of living is also high.