1.'모자라다' is a verb and '부족하다' is an adjective. e.g. 모자라는 것이 있으면...(O) 부족하는 것이 있으면...(X) -> 부족한 것이 있으면..(O) 2. '부족하다' is used when the insufficient status is sustained for a long time. But '모자라다' is used when the result of a change is below the basic level. e.g. 우주에서는 산소가 부족해요.(O) 우주에서는 산소가 모자라요.(X) 3. '부족하다' can be used also for an ansence of something, But '모자라다' is used for a shortage of something. e.g. 저는 형에 비해 키가 약간 모자라요.(O) 저는 형에 비해 키가 약간 부족해요.(X) 우리는 물이 모자란다 means "Although we have some water, we are short of wather" 우리는 물이 부족하다 means "We don't have any water" or "We are short of wather" 4.'모자라다' can be used also for a person who has a low intelligence or a tactless person. 저 모자란 놈!(O) 저 부족한 놈!(X)

While they are synonyms, 모자라다 sounds colloquial and suits concrete comparisons well whereas 부족하다 can have a more formal feel. 모자라다 also means "dumb" or "retarded" when referring to a third person, which 부족하다 does not. For example, - 케이크를 만드는데 설탕이 모자랐다/부족했다 (모자라다 works better in everyday situations like this). - 그 사람은 참을성이 부족하다/모자라다 (부족하다 suits abstract meanings better). - (저는) 부족하지만/모자라지만 최선을 다하겠습니다 = I have my own shortcomings but I will do my best. - 그 친구는 조금 모자라 = He's a bit of a retard.