In their announcement of the latest Windows 10 insider preview build (18317) Microsoft has revealed their separation of Cortana from Search. The news was posted on the Windows Blogs site this morning:
Yes, this is Microsoft's official graphic from the announcement
"Going forward, we’ll be decoupling Search and Cortana in the taskbar. This will enable each experience to innovate independently to best serve their target audiences and use cases. Some Insiders have had this update for a few weeks now, and we appreciate all the feedback we’ve received about it so far! For those new to this update, when it rolls out to you, you’ll find clicking the search box in the taskbar now launches our experience focused on giving you the best in house search experience and clicking the Cortana icon will launch you straight into our voice-first digital assistant experience.
Other available Search and Cortana settings have also now been split between the two, along with the familiar group policies."
Whether or not this change means that Cortana can be removed entirely without removing Search remains to be seen, though the known processes for completely disabling/removing Cortana are currently more involved than just unchecking a box in settings, to say the least.