People with glasses have the lenses covering their whole eyes. The light they are viewing is refracted, but when the glasses are being worn, they do not notice this refraction since there is no reference point that they can look at (outside the frame of the glasses) to compare the refracted image with the original external objects. But if you were to lower the glasses so that you can see both the image produced by the lenses, and the external objects, you will definitely see a difference between this and the refracted image. In fact, some people who wear glasses may even experience a distortion of their peripheral vision since the glasses image objects directly in front and not on the sides.
Another thing to note is that people who wear glasses for the first time will notice changes in depth perception and sizes/distances may seem different.