2560 x 1600 is more than "fullHD" or whatever marketing terms they use these days (or those days). 1080p - is often called "fullHD" and is 1920 x 1080 resolution.
QuadHD is quad (4x) 720p or 2560 x 1440 resolution.
The old high def resolution is 2560 x 1600 - this is the resolution of old professional or similar monitors -such as Apple's old 30" cinema display.
2560 x 1600 (or there abouts) requires dual link DVI. Most high end video cards had at least one of these ports. HDMI and Display Port should also be able to support these resolution and possibly higher - depending.
4K (also known as UltraHD) is much higher resolution at about 8mega pixels - or around 3820 x 2160 (though full 4K is a bit higher). Many systems only push 4K at 30Hz - though 60Hz is much more common now, your mileage may vary - void where prohibted!
5K is higher still at around 14 megapixels but takes a lot of computational/gpu to run well ...