How does proxy server know the target domain of the client?

Question

I'm currently writing a proxy server in nodejs. To proceed, I need to know how to reliably determine the originally intended domain of the client. When a client is configured to use a proxy, is there a universal way that the client sends this information (e.g. one of the two examples below), or is it application specific (e.g. Chrome proxy settings may do it differently to IE proxy settings, which may be different to a configuration for a proxy for an entire Windows machine, etc.)?

An HTTP request to the proxy server could look something like this, which would suffice:

GET /something HTTP/1.1
Host: example.com
...

In this case, the proxy could get the hostname from the 'Host' header, get the path in the first line of the HTTP request, and then have sufficient information.

It could also look something like this, which would suffice:

GET http://example.com/something HTTP/1.1
...

with a FQDN in the URL, in which case the proxy could just retrieve the path of the HTTP request in the first line.

Any information regarding this would be greatly appreciated! Thanks in advance for the help!