Generally speaking the difference between psoriasis
and "dandruff." Can be clinically differentiated by a dermatologist
, based on appearance and location(s) of the affected area(s). In simplest terms, if the rash is on your body arms, or legs, its unlikely to be dandruff (because dandruff usually only affects the scalp on your head, and sometimes the face if there is a seborrheic dermatitis component involved).
Psoriasis is most commonly an autoimmune disorder
that causes scaly patches of rash to appear most frequently over the extensor surfaces on your body (shins, elbows, etc). It is a chronic condition that can come and go over the course of one's life. Treatment focuses on symptoms control, as there is no clear way to definitively get rid of psoriasis (unless it is thought to be due to a specific drug reaction, which is rare).
Dandruff is scaling and peeling of dry skin from the scalp. If you have other areas affected on your body (such as arms, legs) then its unlikely to be dandruff. There is also an entity called seborrheic dermatitis which can affect the scalp and the face (folds around the nose, cheeks, forehead). Dandruff and seborrheic dermatitis are generally treated the same way.
I would recommend you see a dermatologist for an evaluation of your rash. A dermatologist can narrow down the diagnosis and come up with a treatment plan that is convenient to you.