Office is just another way of saying small room, sometimes it's not big enough to be a proper bedroom so they say office/study so people understand that its a small room which you can use as a place to do your homework, or use as a storage room etc.

Actually, it probably is referring to an office in the sense of where you do your work. Many people have home offices if they do a lot or all of their work from home. Also, the correct term is simple a/the "study" (not a study room), which is a little different. :)

Thank you, Gertie. That's very kind of you sharing explanation in detail and taking trouble corecting my erro. What you have done are both important to me. The material is in an English book and is without a picture to refer to. But I think I get the idea.I plan to share both to my students in class and let they juge themself on this open question.

Also, "What does "office" refer to?" or "What is "office" referring to?" are both correct, but "What is "office" refer to?" is incorrect.

"office" and "study" can overlap in meaning/purpose. Dictionary: a study is "a room used or designed for reading, writing, or academic work"; an (home) office is "a room... used as a place for commercial, professional, or bureaucratic work"; a (home) studio (here's a new, related word) is "a room where an artist, photographer, sculptor, etc., works". "studio" does have multiple meanings, but this is the meaning related to this discussion. A studio is basically an office where certain professions do their work (a police officer doesn't work in a studio but an artist does). A studio could be at one's home, it could be a type of housing, or it could be a completely separate building/place outside of one's home.