How far can a 50 mm lens shoot
Shoot 50mm EF against EF-S
The difference between the EF 50mm f / 1.8 II and the EF-S 18-135mm f / 3.5-5.6 IS is not in the focal length or the angle of view provided by each lens when both can be used on an APS-C housing. The special thing about the EF-S lens is that the image circle projected by this lens is smaller than the image circle projected by the EF lens. The EF lens must project a larger image circle to cover the larger sensor of a full frame (FF) camera. However, the extra portion of the image circle of the larger EF lens compared to the smaller image circle of an EF-S lens is outside the edges of the APS-C sensor on your Canon EOS 550D.
Since a Canon APS-C sensor is typically around 22.5 x 15 mm, the diagonal width of the sensor is around 27 mm. The diagonal width of a 36x24mm full frame (FF) sensor is a little more than 43mm. The EF-S lens only projects a circle just big enough to cover the 27mm diagonal of the APS-C sensor. An EF lens, on the other hand, has to provide an image circle large enough to cover the 43 mm diagonal of an FF sensor.
I think where you are confused is the assumption that the same field of view (FoV) is included in both the 27mm image circle of the EF-S lens and the 43mm image circle of the EF lens. That's not the case. The inner 27mm of the larger image circle projected by a 50mm EF lens contains exactly the same FoV as the entire 27mm image circle projected by the 50mm EF-S lens. This means that if you put the EF 50mm lens on an FF camera, the FoV that the same 50mm lens delivers on an APS-C camera will be in the middle of 40% (in terms of The outer 60% is from the part of the image circle that is projected beyond the edges of the smaller APS-C sensor when the same lens is used for the APS-C body. On the other hand, if a lens (17mm in this case) providing an EF-S size image circle is mounted on an FF body, the circle will not cover the entire sensor.
The white rectangle shows the part of the image circle that would fall on a Canon APS-C sensor. At the same magnification, the same photo would look like it was taken with an APS-C camera.
Only when we bring the image from the APS-C camera to the same size as the image from the FF camera do we see the imprecisely named one 1.6 times the focal length multiplier.
See also Why do full frame lenses and crop body lenses have the same crop factor when used with a crop body camera? and this answer to what is harvest factor and how does it relate to focal length?
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