Nikon VR and Canon IS - Please help me get this straight ...

It doesn't exactly work like that ...

If you can hand-hold and get a clear shot at 1/30 sec without VR/IS, then using VR/IS, you could theoretically get a clear shot at 1/4 sec (assuming f/stop and ISO are the same).

IS/VR allows you to shoot at slower shutter speeds and has nothing to do with focal length.

There are several potential sources of »blur« in images, camera shake and motion blur. Camera shake is what happens when the camera moves significantly during exposure of the image. Then the exposed image is really an overlay of many, slightly shifted images which reduces the perceived sharpness of all of the image. You can reduce camera shake by choosing a faster shutter speed, improving a more steady grip, use of a tripod or by a lens with image stabilization. More on that below.

Motion blur on the other hand happens if the subject moves during the exposure, even though the camera is fixed. Think of a race car or another fast-moving object. The only way to reduce motion blur is to select a faster shutter speed. In practice, this means you either have to get a faster lens (so you can trade a larger aperture for a faster shutter speed) or cranking up the ISO setting on your camera. Image stabilization will help you zilch here.

Image stabilization has many names, Nikon calls it VR, Canon calls it IS, Sigma uses OS. There are two main methods: either you stabilize a particular lens or you stabilize the sensor. If you stabilize the lens, you insert movable optics in the lens which counteracts any camera motion that is detected. Other manufacturers such as Olympus stabilize the sensor rather than the lens, i. e. the sensor's position can be adapted to compensate for camera movements. Then every lens is stabilized, but Canon, Nikon et al claim it is less efficient. Again, image stabilization allows you to significantly reduce motion blur, the marketing material claims an improvement of 2-4 stops.

While it is debatable if it is 2, 3 or 4 stops, ultimately, in most practical applications, the usefulness of image stabilization is limited by motion blur of the subject.