Does Mac have an display driver to go for higher resolution (than the current display)? It used to be on a PC, when hooked up to a 1024 x 768 display, I can actually set the resolution to 1600 x 1200, and the display driver will pan to different part of the 1600 x 1200 section depending on where my mouse moves to.

Can a Mac do that too?  That is, if a Macbook Air only has a resolution of 1440 x 900, can I install some driver to have a resolution of 4k or 5k, and just have the 1440 x 900 showing the section of the 4k or the 5k screen, depending on where the mouse is?

I am looking for this function mainly to sometimes capture some screenshots when reading digital magazine using Zinio the web app, and want to capture the screenshot in 4k or 5k resolution even when the Mac is not hooked up to such display.
Apple, generally does not release drivers other than what ships with OS X. And video card manufacturers generally do not release drivers for their devices installed in a Mac under OS X unless it is a PCI card or some such that has a chipset not specifically supported by OS X.

I suppose the Hackintosh community may have some drivers that do that but I would tend to think that what you are looking for is not available under Mac OS