Camera motion is usually measured in terms of angular size or arc: that is, how many degrees, minutes, seconds of arc the optical axis moves during the time the shutter is open. How much the same amount of motion affects the image is also determined by the angular size of the Field of View (FoV) yielded by a particular focal length and film/sensor size.

For the example in your question: At 1/250 second using good handheld techniques the amount of blur will depend upon the FoV. If you are using a wide angle lens such as one with an 18mm focal length, there will probably be very little detectable blur. If, on the other hand, you use a 600mm focal length there will probably be significant blur, especially if you are using an APS-C camera that reduces the FoV to the equivalent of a 900mm or so lens mounted on a 35mm format camera. The reason for this is that the same objects at the same distance from the camera cover over 1,000 times as many pixels using a 600mm lens as they do using an 18mm lens! (33.33*33.33=1,111.11)

Back in the days of 35mm film, the general rule of thumb was to use a shutter speed no slower than 1/focal length when hand holding the camera. This assumed a print display size of 8x10 inches viewed at a distance of 10 inches by a person with 20/20 vision. With digital sensors that are typically smaller, the crop factor (sometimes called the focal length multiplier which is a term that is more than a bit misleading) must be applied as well (1.5x for Nikon APS-C, 1.6x for Canon APS-C cameras). This still assumes the same viewing conditions, however. If you're going to view sections of the image at 100% on your computer monitor, then even the slightest blur that isn't detectable in an 8x10 at 10" will be evident.