Images can be compressed to take up less space; most image formats automatically include this feature.
There are two general categories of image compression. A lossless method is guaranteed to produce exactly the same picture elements (pixels) that went into it. A lossy method produces an approximation of the original image data.
If you had a photograph of the Great Wall of China taken on a high-end camera, you might end up with:
a RAW image which is very large and completely uncompressed
a PNG image which is quite large but compressed losslessly
a JPEG image which is medium-sized and looks pretty good but is flawed under magnification
a JPEG image which is quite small and doesn't look very good, to be used as a thumbnail
Of these, the byte-for-byte comparison would not call any of them duplicates, but the pixel-by-pixel comparison would call the RAW and PNG versions the same image.