Modify the `Host` header or pass `X-Forwarded-Host` instead when using Nginx as reverse proxy?

Question

I'm trying to use Nginx as a reverse proxy and the upstream server is an ASP.NET Core application where I've registered the ForwardedHeadersMiddleware, which will read three different X-Forwarded-* headers:

• X-Forwarded-For
• X-Forwarded-Proto
• X-Forwarded-Host

Now, I understand the first two, but find the last one (X-Forwarded-Host) confusing. I've seen Nginx reverse proxy configurations usually rewriting the Host header like so:

location / {
    proxy_pass http://app;
    proxy_set_header Host $host;
}

But then I've also seen the X-Forwarded-Host being used instead:

location / {
    proxy_pass http://app;
    proxy_set_header X-Forwarded-Host $host;
}

In some cases both are used at the same time:

location / {
    proxy_pass http://app;
    proxy_set_header Host $host;
    proxy_set_header X-Forwarded-Host $host;
}

I'm not sure what I should do. Why would you use both at the same time? And why would anyone use the X-Forwarded-Host header if they can simply change the Host header directly? I've noticed that the result in my ASP.NET Core app will be the same regardless of whether I set Host or X-Forwarded-Host (or both), in either case, HttpContext.Request.Host is set to the expected value — provided that the forwarded headers middleware is registered, of course.

To my surprise, I couldn't find any relevant information on this issue by googling, so I had to ask this here. What is the right approach to take in this situation?