I had originally been taught that "부엌" means kitchen, but recently I came across this word "주방." What is the difference between these two words? Are they typically interchangeable, or are there situations when its only appropriate to use one and not the other?
When the National Korean Language Institute (국립국어원, the official government authority on Korean language) was asked this same question, they did not indicate any major difference between these two words.
부엌 is pure 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.
Generally, pure Korean words are more colloquial and used more often in everyday conversation, while Chinese character words are more formal and used more often in written documents.
Although there is no direct analog for "kitchen," I would consider the difference similar to the one between "bathroom" and "lavatory" in English. (부엌:bathroom::주방:lavatory.) Sometimes one sounds better than the other; you can usually interchange them without greatly changing the meaning. A Korean analogy might be 부엌:사람::주방:분.
If you are interested in references/sources for the difference in usage of native Korean words versus Sino-Korean words (words derived from Chinese characters):
Sino-Korean words today make up about 60% of the Korean vocabulary, though in actual speech (especially informally) native words are vastly more common.
Source: https://en.wikipedia.org/wiki/Sino-Korean_vocabulary (Wikipedia further cites two books.)
It is not unusual to find native Korean and Sino-Korean words with similar or overlapping meanings. When this happens, the native Korean word tends to be more colloquial, while the Sino-Korean word is usually more formal and literary. (e.g. 엄마/아버지 versus the formal and impersonal 모친/부친)...
The majority of the vocabulary used in written materials such as newspapers, magazines, documents, and books is of Sino-Korean origin. The same is true of news broadcasts, lectures, and ceremonies, as well as just about any conversation on a topic that goes beyond ordinary life.
This passage is followed by numerous examples.
This book gives an explanation of why this might be so:
The vocabulary of Korean has two principal sources. Approximately forty-five percent of its words can be traced back to Middle and Old Korean. These so-called 'native Korean' words tend to denote things and concepts central to everyday life--body parts, traditional foods and cultural practices, kinship relations, basic actions, native plants and animals, and so forth.
Choo, Miho, and William D. O'Grady. Handbook of Korean Vocabulary: A Resource for Word Recognition and Comprehension. Seoul: Hanguk Munhwasa, 2002. Ix. Print.
I think another influence was that the use use of hanja was historically limited to the upper class. Similar to how French/Latin-based words tend to be more formal ("lavatory") in English compared to their Germanic counterparts ("bathroom").
Here(link), there you go.
주방, 부엌, 취사장 모두 음식을 만드는 공간을 가리킨다. 어디에 있느냐에 따라 달리 불린다. 부엌은 주로 일반 주택에 딸려 있을 때를 말한다. 주방은 식당과 같은 요식업소에 있는 것을 가리킬 때 사용된다. 아파트나 현대식 주택에 딸린 것을 뜻할 때도 있다. 취사장은 많은 사람이 공동생활을 하는 곳에 있는 것을 뜻한다. 취사장은 규모가 큰 것을 가리킨다.
There are three words; 주방, 부엌, 취사장.
All of them mean a place in which food is cooked. We can gage what to use according to buildings where it is.
부엌 is used when the place is in the residence. For example, your house or friends house. Or apartment, condominium. That kind of thing.
주방 is used when the place is in the restaurants. Sometimes it's used when the place is in apartments or modern residence, though.
취사장 is used when the place is in the community place such as school and military service. It is quite big size.
I think this information is fairly correct according my experience. At home, I use 부엌. At restaurants, I use 주방. I used 취사장 when I served my military service.