the truth behind the search

I've been reading Linked for LIS 2000. It's a very interesting approach to talking about networks and how nodes are linked to each other. Many of the illustrations in the book we've talked about in LIS 2600 especially the history of the Web, virus, operating systems, etc. Anyway, the reason I am even bringing this up is I am completely shocked by the fact that Yahoo! fired Inktomi (the company that ran their search engine) in 2000 and hired Google instead! Maybe I'm clueless and this is a well known fact, but this is so incredibly interesting to me. I can remember when Google first became big and everyone was fighting about which search engine was better Google or Yahoo! If this information is correct they are one in the same! Yes, they are separate companies, but if Google runs the searches for Yahoo! shouldn't relatively the same results pop up with the same search? Now my question is does Google still run the searches for Yahoo!?? I think I shall go Google this answer...