abnormal = often a negative connotation of being different. The mole on your back needs to be checked out. It seems abnormal. Uncommon = a difference that is not necessarily strange nor negative It is uncommon to play cards as well as she does.

uncommon =Not common, rare,Wonderful, remarkable. abnormal= not normal, average, typical, or usual. deviating from a standard: abnormal powers of concentration; an abnormal amount of snow; abnormal behavior. extremely or excessively large: abnormal profit.

Uncommon refers to something you don't see or hear very often. Abnormal refers to the same thing but can also be a synonym for 'strange'. Abnormal :not normal; not typical or usual or regular or conforming to a norm; "abnormal powers of concentration"; "abnormal amounts of rain"; "abnormal circumstances"; "an abnormal interest in food"