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 terms of focal length or angle of view provided by each lens when both are used on an APS-C body. What makes the EF-S lens different is that the image circle projected by that lens is smaller than the image circle projected by the EF lens. The EF lens must project a larger image circle in order to cover the larger sensor of a Full Frame (FF) camera. But the extra part of the larger EF lens' image circle, when compared to the smaller image circle of an EF-S lens, falls outside the edges of the APS-C sensor in your Canon EOS 550D.
Since a Canon APS-C sensor is usually around 22.5x15mm, the diagonal width of the sensor is about 27mm. The diagonal width of a 36x24mm Full Frame (FF) sensor is a tad over 43mm. The EF-S lens only projects a circle just large enough to cover the 27mm diagonal width of the APS-C sensor. AN EF lens, on the other hand, must provide an image circle large enough to cover the 43mm diagonal width of a FF sensor.
I think where you are getting confused is at the assumption that the same Field of View (FoV) is contained in both the 27mm image circle of the EF-S lens and the 43mm image circle projected by the EF lens. This is not the case. The inner 27mm of the larger image circle projected by a 50mm EF lens contains the exact same FoV as the entire 27mm image circle projected by the 50mm EF-S lens. What this means is that if you put the EF 50mm lens on a FF camera, the FoV provided by the same 50mm lens on an APS-C camera will be in the middle 40% (in terms of area) of the frame, and the outer 60% will be 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 on the APS-C body. On the other hand, if a lens (in this case 17mm) that provides an EF-S sized image circle is mounted on a FF body, the circle doesn't cover the entire sensor.
The white rectangle shows the portion of the image circle that would fall on a Canon APS-C sensor. With magnification at the same level, the same photo would look like this taken with an APS-C Camera,
It is only when we make the image from the APS-C camera the same size as the image from the FF camera that we see the inaccurately named 1.6x focal length multiplier.
See also Why do Canon EF and EF-S lenses exhibit the same crop factor? and this answer to What is crop factor and how does it relate to focal length?