If it is the same manufacturer's identical radiator there is a chance the same brackets are used. However ,manufacturer's do tend to change things over the years ,so if your existing rad is ten years old ,it's more likely the brackets will be different.
Usually the thickness of the same type of radiators are very similar (11/21/22) so the pipe centres from the wall should be close enough as makes little difference. Only when going from different types will the centres from the wall be different.
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