I once tried to use one note for taking notes for work (1:1s, etc.) on a surface pro 4, and found that unless you go to great lengths, OneNote does everything it can to sync your notes to OneDrive. Even after turning off sync for specific books, those books ended up in OneDrive. In the end, I had to uninstall onedrive, disable syncing globally, and then login to OneDrive to delete the previously synced copies.
So users that care about privacy in their notes beware: it does take a bit of work to turn off all of the cloud functionality.
That sounds like the free version of OneNote that comes with Windows 10. The "full-fat" desktop version that comes with Office ("OneNote 2016") is much more flexible in this regard, and has a more powerful interface.
So users that care about privacy in their notes beware: it does take a bit of work to turn off all of the cloud functionality.