Evidence gathered in relation to one benefit can be used in relation to another. (For comparison, information about your finances gathered in relation to one benefit can be used in relation to another benefit, even if it is paid by a different body, e.g. council, revenue etc.)
Although the criteria are different, there are overlaps. For example, how far you can walk would be relevant. To take an extreme example, if you claim DLA mobility on the basis that you can't walk at all, and then you are found at an ESA medical to run marathons, you are likely to find that your DLA is reassessed. Of course, most examples are rather less extreme, but the principle is the same.
