Ah, one of those questions that I always like to ask controllers when I am hanging out with them. A bit like 'when you ask me to report a "two mile base", is this two miles from the tower, two miles from the end of the runway, or two miles from the base/final turn'. And I never get the same answer.
For me, I always use "final" with a distance i.e four mile final EXCEPT when I am close to the threshold and landing is imminent. So then I'll report 'Short Final' to ATC if they haven't yet cleared me to land, or on the common frequency if I'm landing next and nobody better get in front of me or decide to depart. Long Final means nothing to me, if I heard it on a common frequency I'd ignore it as a means of locating somebody (but keep a look out for somebody who I thought was a risky person to share a pattern with and is out there somewhere). It's also easy to ask him on the frequency how far he was out, then bear that in mind while looking.