안녕하세요 리더님! Koreanstudyjunkie입니다~
부엌 is pure Korean - Native Korean, and 주방 (廚房) is derived from Chinese characters. They mean the same thing, so it is a matter of personal taste and they can be interchanged without greatly affecting the meaning of a sentence.
Native Korean words are more colloquial and used more often in everyday conversation, while Sino words are more formal and used more often in written documents.
That being said, 주방 is used more often for restaurants and big establishments. While, 부엌, is used more often for kitchens inside people's homes or apartments.
You can use them interchangeably in daily conversation!