"What did the teachers use?"
Translation:선생님들이 무엇을 썼습니까?
사용하다 is strictly "to use" it's also a little more formal and used more in written Korean.
쓰다 is used more in spoken Korean and can mean many different things depending On the context. 편지를 쓰다 (to write a letter) 이 연필 좀 쓰세요 please use this pencil 이 말을 어떻게 쓸 수 있어? How can I use these words?
이 커피가 너무 써요! This coffee is too bitter!
It can also mean to wear something like glasses. 안경을 쓰다 To wear glasses.
Source: Mel (Hinative, Oct 2016)
they have a big overlap in the definition of "to use
an object for a purpose"
but ill say that 사용하다 is more limited to just that "utilize" function.
ill give two examples of where it would be awkward
to use 사용하다 in place of 쓰다 to mean "use"
'그 장난감을 사려고, 돈을 쓴다' i use money to buy the toy.
you arent utilizing money as a tool, you are expending it. using it up.
'그 사람에 대해 신경을 안 쓴다' i dont care about that person.
신경 is nerve, but to "신경을 쓰다" "use a nerve" is an idiomatic
expression for "care" or "give a damn", using 사용하다 here
would be odd for the same reason.
right away ill add on top of all that, technically speaking, 쓰다 has
three different definitions as a verb, and 20 different usages across
those three verbs. dont freak out, but you will see it in other places.