But what does "Windows-style fullscreen" actually do? It feels like it switches into a different video mode (even if the resolution is the same), and back when my monitor was a CRT, I could even hear a faint click inside it whenever a game entered/exited the full-screen mode. So there was definitely something special going on, but what?
Windows style fullscreen made it so that the game controlled the resolution being sent "over the wire" to the display, and as I understand it, basically gave exclusive display access to the game. This had the interesting effect of delegating all resolution scaling to the display, which was great for CRTs and often very bad on digital displays which (usually) do very muddy bilinear scaling even if being sent a resolution that was an exact integer division of the total display resolution.
The current day approach is to instead do the "large borderless window" and then do software scaling of the image in order to match the display resolution. One cool result of this is you can get much better scaling than your display would do naively. Low-res games really benefit from software integer scaling instead of "whatever scaling the display firmware does, usually making all the edges blurry".
Rescaling in software is so fast now that some graphically intense games can do per-frame scaling in order to keep per-frame latencies below a particular goal threshold, at the cost of your game losing fidelity (getting blurier). It's so common that most big-name titles now do this.
