"Something has changed while I was sleeping" => 자는 동안에 무언가(가) 변했어 / 무엇인가 달라졌어.
아무것 is "anything", as in 뭐 먹고 싶어? / 아무거나 줘요 (Give me anything).
A simple rule is: something: 무엇, anything: 아무것, everything: 모든 것, nothing: (no matching word - 아무것도..아닌..).
무엇 means "what" in questions, and "something" otherwise.
When emphasizing the "unknown" nature, the "~인가" suffix is often added(무엇인가, 어딘가, 어디선가, 누군가).
So there are a few variations centered around 무엇 (what; something).
- 무엇인가 -> 무언가 -> 뭔가: emphasizes it is not definable.
- 무엇인지 -> 무언지 -> 뭔지: (similar)
- 그 무언가: "that something" - another way to emphasize it.
Here's an example usage of 무언가 (from a song):
- 어딘가 있을 무언가를 아직 찾고 있다 했지.
=> I said I was still searching for that something (that must be) somewhere.