There are two different things here, and they are treated differently. Moisturizing healthy skin is advised. Applying things to a scar is not.
For healthy skin, the advice is consistent. Caring for healthy skin by keeping it clean and moisturized is one of the ways to avoid further injury from pressure sores. With venous ulcers, protect the skin around the wound by keeping it clean and moisturized. To help prevent venous ulcers, keep the skin of your lower legs well moisturized.
Diabetes foot care is the most specific about what to use, and it carries an exception. Use lotion, petroleum jelly, lanolin or oil on dry skin. Do not put lotion, oil or cream between your toes unless instructed to do so by your provider.
The scar itself is a different question, and the answer is less encouraging than most people expect. Once the scar forms, some people think it helps to massage it with vitamin E or petroleum jelly, but this is not proven to help prevent a scar or help it fade. Do not rub your scar or apply anything to it without talking with your provider first.
So keep the skin around and beyond a healed wound in good condition, as ordinary skin care. For the scar itself, talk with your provider before applying anything.
Why the first half matters is in what moisturizing is listed next to. For pressure sores, it sits alongside checking the skin daily and relieving pressure. For venous ulcers, it sits alongside compression and elevation. It is there as part of keeping skin intact, which is to say part of not having the next wound.