Both are explicitly related to the web at large. Google sells ads on more than two million sites, and those mostly aim to be the kind of sites that feature in search results. I'd say that the two code bases are related, by virtue of operating on the same data structure.

You remember the pagerank paper? It described how Google classifies each page on a scale from "something that links to good pages" to "informative page". Google and other search engines produces links to the latter. And since then, web site operators have had strong incentives to be on the "informative page" end of the range. Today I don't think the 2000s code can find a lot of pages of the former kind (well, outside Facebook).

It produced very nice results back then. It was/is good code, but good results need more than just good code, it needs good input too.