On a multi display desktop with Cortana disabled (Desktop mode, taskbar showing on all displays, taskbar on the bottom of the screen), the primary display has the "Search Windows" search box, and any additional displays have the magnifying glass or search icon as pictured below.
You can change the primary screen to this symbol by right clicking the taskbar -> Search -> Show search icon - as per below (if you want to save some real-estate)
I think with Cortana enabled that is replaced with the Cortana symbol.
Update 10 May 2018
With each version of Windows 10 Cortana has become more difficult to disable. The 'Search' option when you right-click on the main toolbar has been replaced with 'Cortana' - the same options apply. It also looks like the default behaviour is to include Cortana on all taskbars.