Confused about past tenses

Hi,

Can someone please give me a definitive explanation on the use of the present perfect? I am a bit confused right now.

I understand that there are differences in the way Americans and British speakers use it. For example.
(Am. E.): "She has a stomach pain. She ate too much."
(Br. E.): "She has a stomach pain. She has eaten too much."

So why not:
"This is John, a playwright. He wrote three plays."
"This is John, a playwright. He's written three plays."