Gamut and color count are not really the same thing, although a low bit depth will start to affect gamut to a degree (i.e. a 6-bit flat panel will never be wide gamut, simply because its sampling of the color space is too sparse.)

Gamut describes the range of colors, from the total Lab* space, that a monitor is capable of representing. Many monitors are only capable of reproducing the sRGB space, which would be "standard" rather than "wide". Anything that approaches or surpasses the AdobeRGB space is "wide". It is important to note that even though sRGB monitors are not wide gamut, it is still capable of displaying 16.7 million colors just like a wide gamut display.

The difference is the "extent" of the mapping of those colors. On an sRGB display, the most saturated and pure green will not be as saturated and pure as the most saturated and pure green on an AdobeRGB display. (See image above for mapping extents of sRGB relative to AdobeRGB and the full visible color space, or Lab). Similarly, although to a lesser degree, the same goes for the most saturated reds and blues. Having a wide gamut display means your colors can be richer, purer, and more expansive, even though the screen still displays the same number of colors.

It should be pointed out that with displays that use RGB LED technology, the source light itself is purer, and allows gamut coverage of over 100%...sometimes as high as 130-140%. Combined with higher bit depth of 10 bits, these displays are capable of displaying at least 1.07 billion colors with considerably richer, smoother rendition of a more extensive and complete color palette. Such a display would be ideal for photography.

As for the specific monitor you have linked, I see no evidence it is a wide gamut monitor. It seems to be a fairly standard monitor built with LED backlight technology. I wouldn't expect much more than sRGB performance out of it. To my knowledge, Samsung does not currently produce any wide gamut desktop displays. The only time "wide gamut" is associated with Samsung is in reference to some of its more recent Galaxy smartphones. If you want a wide gamut display, you will need to look into Dell, Apple, NEC, Eizo, etc. Personally, I think NEC has a corner on the price/value sweet spot, with high quality monitors using 14-bit hardware LUT (1.07 billion colors) and high quality hardware calibration for a reasonable price point. Dell offers some screens with 12-bit hardware LUT, however their screens often have an oddball antireflective coating that evokes more hate than love from photographic professionals. Dell UltraSharp screens will be the cheapest "quality" wide gamut displays on the market.