why Invariant moments are slightly diffident for the same image

Please see my comment to the question. Imagine all your calculations are correct, which is pretty likely. It could be just withing the accuracy of the method. But then, if you re-sample some image, it is not exactly the same image. Think of this in this way: you image itself isexpressed in pixel values, is only an approximation of some "ideal scene". Colors are mangled, some may be saturated or be a subject of value discretization. But what is more important to us, the pixels themselves do not exist in the nature: each pixels gets its color based on some averaged value reflecting the light coming from some 3D angle, and also mangled by optical system aberrations; and also, pixels as electronic devices are not independent, they slightly affect each other through some parasitic effects. But what comes from the camera is the single point of truth. What happens when you re-sample and rotate the image in software? Original correlations between pixels are majorly destroyed, and, essentially, you introduce additional discretization error. It will be especially apparent when you upscale the image (which always entails some inherent quality loss). If you read about the algorithm (or even if you won't but just think about it), you will see that some non-existent pixels have to be "created" using one or another extrapolation algorithms. Such algorithms always have some limited accuracy. In other words, you create some new image, only closely resembling the original (or not even so closely, if this is a high magnification). And this image is somewhat different in all its features, including its moments.

—SA