35mm lens on a cropped frame

When I bought my first APS-C sensor DSLR I wanted to buy my first prime lens.

I was told 35mm lens is equivalent to standard normal view 50mm on a 35mm sensor .. and the 50mm will be the equivalent of 75mm ..

I therefore bought the 35mm just to get the surprise of my life .. the 35mm lens did not behave like a 50mm when it came to perspective and distortion .. it kept its usual wider angle perspective .. just being cropped meant the image appeared as if it was more zoomed in due to the cropping ..

I returned the 35mm lens straight away and replaced it with a 50mm that behaved as expected exactly like a 50mm lens and not a 75mm when it came to perspective and DOF .. only the DOF was more deeper compared to the same lens and aperture on a full frame as it took the same shot from further away !!