[Is there much of a difference in the effectiveness of backlinks as they relate to your site? For example, if I do a site for antique British cars, is a backlink from an antique related site or car-related site more powerful than a backlink from the cooking site, given the same page rank? If I hire someone to develop backlinks for me, what should I beware of, or insist on?]
There you go again: “a link from a site about gerbils.”
You just can’t help yourself, can you?
Website topics have absolutely nothing to do with SEO. Search engines never even try to understand what a website is about, only what a page is about.
And yes, we do agree that the elements that are treated as the strongest signals of relevance vary according to the context of the situation. While a page title is arguably the strongest signal of relevance for on-page scoring, the anchor text element is the strongest signal in the context of a backlink.
Where we seem to possibly disagree, just a bit, is whether there are other signals of relevance for a backlink besides simply anchortext. I assert that text near the anchor is also a signal of relevance and to a lesser degree so is the page title and nearby headings. The reason these are different from on-page factors is that Google uses principles of prominence and proximity as part of their weighting factors. The words in and near the anchor text element are more prominent and have closer proximity than other elements within the context of a backlink.
Google’s founders discuss those principles and claim to use them in their algorithm as disclosed by the white papers they produced during the original development of Google’s technology while attending Stanford. It’s been a core part of Google’s technology from the very beginning.
There is a lot that has been disclosed about how Google works. The main thing they have kept secret is how much weight they apply to the various signals of relevance within the overall relevancy score. They are not the mystical magical black box that so many folks seem to suggest they are, at least not if you willing to read about how their technology works and you can understand a little about statistics and a bit of advanced math.