How does international mail service work?

Suppose that someone is mailing me a box from Germany. They go to the post office in Berlin, pay the postage, and the item is on its way.

It obviously gets to an airport in Germany – probably Frankfurt, but possibly not.

Does the Deutsche Post put it on a German plane to the US, under the DP’s authority? Or does the DP give it to the USPS representative in Frankfurt, thereby making the US responsible for it? Does the USPS have to fly it on a US flag aircraft?

I’m curious about where one country’s responsibility ends and the other’s begins.