First of all, let's get this out of the way:
When you say "Windowless Fullscreen", you actually mean "Borderless Fullscreen" or "Fullscreen (Windowed)". Windowless Fullscreen and Fullscreen are the same thing (explanation below).
The main difference is in how the rendered graphics are displayed on screen:
In Fullscreen mode
the game renders directly onto the screen (no window). This is the simplest and fastest way.
In Windowed Fullscreen
the game renders to an off-screen buffer, which the OS then puts into a window (aka. compositing). The window is rendered without borders, maximized, and displayed on top of the OS's own UI elements (such as the Taskbar and whatnot).
Fullscreen exists for 2 reasons:
- Historically, there were no windows back in the days, so games had to render directly on screen.
- In Fullscreen mode, the OS leaves all graphics-related resources to the game. This is also known as "Exclusive Fullscreen" and improves gaming performance. Nowadays the performance increase is marginal, which is why there is an increasing number of games supporting Windowed Fullscreen mode.
As you've noticed yourself, Windowed Fullscreen has plenty of advantages over Exclusive Fullscreen.
Since the OS relinquishes compositing to the game, the game has to give controls back to the OS when the user Alt-Tabs, which is what causes the lags that Windowed Fullscreen mode doesn't have.
Additionally, as a tradeoff for leaving the game with direct access to graphical resources, the game is now responsible for properly handling those resources. Not all games do, which in many cases causes graphical glitches or even crashes, when the player Alt-Tabs back into the game (i.e. the game didn't expect the OS to take back control).
To summarize, here are the advantages of both methods:
- Playing at lower resolutions doesn't mess up with size or positioning of other windows, desktop icons, widgets, etc.
- OS can instantly switch between windows, since it keeps control at all times.
- (Poorly written) games don't assume they stay in control of graphics resources, so they don't behave weirdly whenever the player uses Alt-Tab.