Factitious DO. Neurosis is old term that is replaced by somatization do. Factitious do is one type of it.
Factitious disorder. Is a form of somatoform disorders which are separate diagnoses from psychoses.
Borderline. First of all, it's kind of apples and oranges. Factitious disorder isn't classified as neurotic or psychotic. It's a different categorization system. It can have elements of severe neurosis, verging toward the psychotic at times. People induce symptoms to be in the sick role. It doesn't typically include a delusional-type belief such as in hypochondriasis. Often accompanied by personality d/o.