I have read the following sentences:
의사가 뭐라고 말했어요?
이 약을 하루에 두 번 먹어야 한다고 말했어요
Why does the former sentence use 라고 while the latter uses 다고? My dictionary says both functions like a conjunction that in English. For me the only difference is affirmative vs interrogative, but is my guess correct here?
My dictionary says both functions like a conjunction that in English.
They could both be translated as 'that' in some circumstances, but I'm not sure that's very useful information, as 'that' is a word with many functions and meanings in English.
It might be more useful to remember their function, which is to report speech. English has the concept of indirect and direct reported speech, and so does Korean.
Indirect reported speech is more complicated than direct reported speech in Korean as there are four endings commonly used.
(ㄴ)다고 is used for indirect reporting of declarative statements (straightforward facts):
이 약을 하루에 두 번 먹어야 한다고 말했어요 => She said that I should take the medicine twice daily.
(느)냐고 is used for indirect reporting of interrogatives (questions):
어디 가냐고 했어요 => He asked where I was going.
자고 is used for indirect reporting of propositives (suggestions):
사장님께서 태국에 사무실을 열자고 말씀 했습니다 => the boss suggested we open an office in Thailand.
라고 is used for indirect reporting of imperatives (instructions):
춤을 추라고 했어요 => we were told to dance.
라고 is also used for indirect reporting of structures with the copula, 이다:
나쁜 놈 이라고 했어요 => they said he was a bad man.
Direct reported speech is easier - it always uses (이)라고:
"사랑해요" 라고 했어요 => She said "I love you".
개는 "멍멍" 이라고 했다 => the dog went "woof woof".
"뭐라고" could be seen as a special case. You can see the similarity between 뭐라고 and the other forms using 라고 above, but it might be simplest to think of "뭐라고" as a word you use when asking what someone said - and 의사가 뭐라고 말했어요? is an example of this.
Their usages are very confusing and sometimes they are used interchangeably by native speakers. However, there is big difference you need to note.
앞말이 직접 인용되는 말임을 나타내는 격 조사. 원래 말해진 그대로 인용됨을 나타낸다. A particle that indicates the preceding sentence (phrase) are a direct (word for word) quotation.
For example, if your doctor said, "약을 하루에 두 번 드세요." and you want to quote what he said word for word, you have to use the following sentence.
(의사가) "약을 하루에 두 번 드세요."라고 말했어요. Sometimes the double quotation marks are omitted, but if you put them there, it would be easier to understand.
If you don't need to quote him word for word, you can say
(의사가) 이 약을 하루에 두 번 먹어야 한다고 말했어요.
This sentence just conveys the core meaning of what the doctor said.
If you use
(의사가) 이 약을 하루에 두 번 먹어야 한다라고 말했어요.
it sounds very weird and unnatural because a doctor would never talk down to a patient by saying "약을 두 번 먹어야 한다."
A side note: If the preceding block has no final consonant (받침), you should use '-라고' and if it has, you should use '이라고' as in
팻말에는 “금지구역”이라고 쓰여 있었다. (Literally) "Restricted Area (금지구역)" was written on the sign.
팻말에는 "출입금지"라고 쓰여 있었다. (Literally) "Off Limits" was written on the sign.
