Janco is absolutely correct. First, though, let me correct a misstatement - a 20mm lens on FF is still a 20mm lens on APS-C, you're just cropping away enough of the image circle to result in an angle of view equivalent to 36mm on FF; focal length is an intrinsic lens property, independent of sensor.
As for distortion, that's intrinsic, too, but like many image artifacts (vignetting, lateral chromatic aberration, etc.), it's worse at the periphery of the image circle, and that's the part that's cropped away when using an EF lens on APS-C.
You can see this yourself - head over to photozone.de and pick a lens (easier with a prime, e.g 35/2 or 50/1.4) they've tested on FF and APS-C, and compare values for distortion (or vignetting) - they're always lower on APS-C for the same lens.