As far as 1/125, 1/250, 1/500 'looking all the same' this: in a dim room hold the lens so that it faces a white piece of paper. Because of the dimness, that paper will not be too bright and where your eye is, is even dimmer. Look through the lens (eyes about 12 inches away from the lens): fire at open aperture at all three fast speeds. You should see a marked difference with brightness in this way.

In full room light they tend to 'look all the same' but with 'just enough' light coming through and with your viewing area dim (so that extraneous light does not get in the way), there should be a difference. - David Lyga