Fake full screen removes page tearing because your windows manager is accelerated by the video card and applying vsync already. It also has an advantage of applying color management to games that do not support it properly.
While it works well, it also has issues of stuttering with some frame rates.
G-sync and free-sync have the monitor only draw new frames as they are ready thus eliminating or greatly reducing this issue.
Normally the monitor refreshes at a constant rate so if a new frame is not ready, the old one stays on screen. With vsync off the new one may become available part way though a frame display and this leads to the tear effect.