While users will still look to Google when searching in their web browser, the role of search in the modern operating system is more than the browser. It can be evoked in almost any application, and global search is generally a key-press or a touch gesture away.
For Apple this means Spotlight. In the new versions of their operating systems, Google results will be removed from Spotlight and replaced with Microsoft’s Bing. Of course Apple is going to offer searches through iTunes, the App Store, Apple Maps, iBooks, and more, but the prize of web searches in Spotlight now goes to Redmond.
One of the features of OS X Yosemite due out this fall is how much Spotlight has been moved front and center — literally — and how much more power it’s been given. I’ll likely be opening up far fewer search tabs in Safari, and I suspect that’s exactly the point.