Tax implications of overseas work - contractor vs employee?

We are a nonprofit looking to hire someone (who will be autonomous, but will give work to other employees who are based in the US and in some ways will essentially act as our Executive Director) who is going to do all their work outside of the US. My question:

If we hire them as a independent contractor, do we/they need to pay any US taxes (and which ones)?

If it's an employee, but an employee who is exclusively working overseas, do we/they need to pay any US taxes (and which ones)?

I am also wondering whether there is any distinction b/w hiring as a contractor vs employee in the overseas setting that concerns the US from an employment law perspective.. but that might be outside the ambit of this conversation.

All help greatly appreciated!

A. Hiree is a resident of a foreign country and not a US citizens or US resident alien: You have no US withholding or payment requirement. However, you may have to check with the country where the person is employed as to what their tax requirements are for self-employed individuals. B. Hiree is a US citizen or US resident alien: The answer would also be no to US taxes. A bilateral social security agreement with the foreign country may require foreign social security taxes to be withheld. And as in A, the foreign country may require certain taxes to be withheld and remitted.

A. Hiree is a resident of a foreign country and not a US citizens or US resident alien: You have no US withholding or payment requirement. However, you may have to check with the country where the person is employed as to what they require. B. Hiree is a US citizen or US resident alien: Now it gets complicated. Typically, you must withhold US income tax unless either the foreign country requires withholding foreign income tax or you have a statement from the employee that the income can be excluded as foreign earned income under the bona fide resident or physical presence test. You would also be on the hook for social security and medicare taxes unless there is a bilateral social security agreement that makes the payments subject to foreign equivalent taxes rather than US taxes.