There's little mention about those different words and from what I read here, I ended up thinking that people will unlikely write he's died to mean he has died. However that's my mere opinion.
I digged up more and found this discussion on Quora: Most respondents said both could work and Most respondents said he has died is grammatically incorrect. Sorry, but the more I read them all, the more I'm getting confused as to whom I should trust.
In order to simplify all this, please consider my made-up conversation and I hope you would provide some feedbacks and some relevant explanations.
A: Papa was not coming home last night, was he?
B: Perhaps he's died.
If I were to write a story, could I use the clause he's died that way? Or do I have to use he's dead?