How to redirect to a different domain using NGINX?

That should work via HTTPRewriteModule.

Example rewrite from www.example.com to example.com:

server {
    server_name www.example.com;
    rewrite ^ http://example.com$request_uri? permanent;
}

server {
    server_name .mydomain.example;
    return 301 http://www.adifferentdomain.example$request_uri;
}

http://wiki.nginx.org/HttpRewriteModule#return

and

http://wiki.nginx.org/Pitfalls#Taxing_Rewrites

server_name supports suffix matches using .mydomain.example syntax:

server {
  server_name .mydomain.example;
  rewrite ^ http://www.adifferentdomain.example$request_uri? permanent;
}

or on any version 0.9.1 or higher:

server {
  server_name .mydomain.example;
  return 301 http://www.adifferentdomain.example$request_uri;
}

Why use the rewrite module if you can do return? Technically speaking, return is part of the rewrite module as you can read here but this snippet is easier to read imho.

server {
    server_name  .domain.com;

    return 302 $scheme://forwarded-domain.com;
}

You can also give it a 301 redirect.