I'm having a CW very soon. Of course it doesn't do the same movement as jutting your jaw forward since a CW doesn't move the teeth at all, only the bottom edge of the jaw. See my crudely-made drawing: bone is cut along the blue edge (important: the cut is made below the nerve, this is why the surgeon needs the 3D scan, and why some people with their nerve too low can't get a CW), the detached part can then be moved freely (towards the front and rotated, as shown here, but can also be moved to the side or even back). If necessary, the gaps can be filled by bone that is taken from the inside of your hip. In case of small movements however, the gaps are small enough that bone can grow back by itself. What is worth mentioning here is the fact the the soft tissue stays attached to the bone. That's what makes CW results look more "natural" than say implants.
So back to jutting the jaw. The bone movement isn't the same, but I think jutting the jaw can at least give somewhat of an idea of what a CW can bring. For instance, notice how the jaw looks wider when bringing it forward, even though it's same same width. This is because in its normal position, the angles are hidden in somewhat loose skin, and by simply stretching it you get much more defined contours. On top of that a CW can also make the angle closer to 90°. The new angle is already more aesthetic, but it brings even more skin stretching.
Remember a couple years ago when everyone was doing a duckface in their selfies? It looked quite dumb, but by doing a duckface you automatically jut your jaw and by puckering your lips you stretch your skin even more. This leads to a more defined jaw contour and thus better-looking selfies. I think people unconsciously did it for this very reason.
As Lefortitude said, it's not a substitute for proper jaw surgery if you badly-positioned jaws. But I think that for a lot of cases, it's more than enough to make you look a lot better. The fact that it's a relatively cheap operation and that the recovery time is short (at most 2 weeks) makes it a very attractive choice.
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