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This is how external debt is explained in wikipedia:

"In public finance, external debt (or foreign debt) is the component of the total government debt which is owed to foreign creditors; its complement is internal debt, which is owed to domestic lenders. The debtors can be the government, corporations or citizens of that country."

Government debt is the debt owned by a government or sovereign state to lenders. It does not include the debts of private entities in the country. External debt is a part of government debt. Then how come the debt of corporations or citizens contribute to the external debt of a country?

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The passage on Wikipedia is convoluted. Total government debt is given by sum of foreign and domestic debt issued by the government.

$$ \text{Total Debt} = \text{foreign debt} + \text{domestic debt}$$

Both foreign and domestic debt is issued by the government.

The distinction is made based on who owns the government debt.

If local businesses, citizens or government institutions hold government debt it is domestic debt.

If foreign citizens, business or governments own the debt it would be foreign debt.

For example, I live in the Netherlands. I could buy US government bonds via my bank. If I would purchase some US bonds they would become part of the US foreign debt. The same would happen if some Dutch corporation or Dutch government purchased US debt.

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