TheMadScientist - 4:43 pm on Jun 27, 2010 (gmt 0)
The links on those pages are actually content on those pages.
That means they're off-page factors for the page that's ranking.
They're not on-the-page ranking, are they?
The OP's talking about links on different pages (they're off-site factors too, because they're not on the same site) having more effect than the content on the actual page (they're off-page factors in the world of SEO) and the fact the links have nothing to do with the topic of the content on the actual page ranking.
The content and links and 'stuff' on the page is considered on-page.
Anything not on the page ranking (which definitely includes links on other pages going to the page) is considered off-page.
It's really not that difficult to understand and there's really nothing to argue about if you know the terminology. If you want to try and change it to add some extra confusion to things or 'develop your own language' and confuse people who don't know better then fine, but on-page is what's on the page and off-page is what's not on the actual page if you talk with people who know anything about SEO.
A really easy way to understand the difference between on-page and off-page is to simply view the source code of any web page and print it out. If it's there it's an on-page factor. If it's not there and influences the rankings of the printed page it's an off-page factor.