They don't, but they share one common goal: Get money from advertisers, who are targeting people looking for some thing.
This "some thing" is obvious on Google, its users are in buying mode even before entering the query term.
Now, if (and that's a big if), FB can connect advertisers and buyers, it'll slow down Google, because people will have spent their money with FB advertisers.
Google and FB customers are their advertisers. They might do completely different things but their revenue source is similar.
I personally don't believe in this. Facebook doesn't share the same easiness of monetization as Google, and it has some huge issues of making its visitors enter buying mode.
But there you go... even if I disagree, that's why some people think of a FB vs. Google fight. Follow the money :)