ELI5 Postage Stamps - does the sending or receiving country get money from my stamp?

If I send a letter or postcard from the UK to the USA, who gets money from my stamp? Once it reaches the receiving country, what makes them obliged to deliver my letter if they are not receiving payment for it? When was the global system for postage established? How does overnight shipping get where it's going faster than a normal package? Why not make everything overnight?

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