I'm not sure why the distinction is unclear?
The term disorder is often used to refer to a condition that causes distress or functional impairment or harm to others, and therefore may require diagnosis and treatment or accommodation. It is not synonymous with 'mental illness', and a large number of conditions classified as psychological disorders would not appropriately be described that way (e.g. autistic spectrum disorders). As we know from discussion elsewhere, the DSM defines numerous conditions that are only considered disorders if they cause distress/impairment/ or harm to others. Psychotic disorders are a subset of disorders that involve symptoms like hallucinations and delusions or disorganised thought, that could impair judgement.
There has been interest in the possibility that body integrity dysphoria involves some sort of inversion of the process involved in phantom limbs (where somebody is missing a limb and feels that it's still there). In the case of phantom limbs, the generally favoured (although still controversial) explanation is neurological - that each part of the body is 'mapped' onto a region of the sensory cortex, and the part of the brain devoted to mapping stimulation from the missing limb, receiving no sensory input, starts responding to stimulation in adjacent regions, which is misinterpreted as coming from the 'phantom'.
If the reverse is true, some parts of the body not being properly 'mapped' might lead to the sensation that a limb is not part of the body because the brain doesn't properly process sensory input from that part.
There seems to be some
recent research along these lines, although the explanation is more complex and relates the issue to altered connectivity in larger scale networks.