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This damage is the corruption.
The way files work is a bit complicated but I'll try to explain. Imagine your hard drive as a filing cabinet with several drawers and loads of individual scraps of paper in every draw. Each scrap of paper is a bit. A file is made up of bits. Now you'd think that the bits would be stored next to eachother in a sensible and organised way but they're not. They are scattered throughout the filing cabinet.
So... you want to open a photo? What you need to do is find thousands and thousands of specific bits of paper in all the drawers of the cabinet all at once and then putting them together in the right order. To do this you have an indexing system. This system tells you exactly where every single scrap is so you can find them. If you lost part (or all) of that index you'd never be able to find all the right scraps. Or if you lost some of the scraps of paper you would never have a while file. This is what happens when files corrupt.
What is happening is that the PC has been able to locate the first bits of data but then either a bit is missing or the index is damaged and it can't go any further. It knows the dimensions of the image (and that the file is an image) because that information is stored in the first bits but when it runs out of info it just fills the rest in grey as it can't find any data.
When you format a disk (or card) you don't actually remove the files, just the indexes so you can't put the files back together. Then, over time, the scraps are re-used and over written. When you try to recover deleted or formatted files you're actually trying to restore the index and the links between the bits. But if some of the bits have been overwritten already or you can't reconstitute the indexing tables properly you won't get the whole file. Only parts of it.
Edit: For clarity the "indexes" I referred to here are the NTFS or FAT32 tables I referred to in my earlier post
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