중국어 - Chinese language 한자 - Chinese characters 한자어 - Sino-Korean language(???)
한자어(漢字語) in the Korean language simply indicates a group of words based on Chinese characters or words, as opposed to 고유어(固有語) or 순우리말, both point to the other group of native-oriented words.
Here, the words "고유어" and "순우리말" are synonyms, but the word "고유어" is a 한자어, while the word "순우리말" is a 고유어.
And of course, not every word either has Chinese-origin or is native-oriented. Thus there's the third group, 외래어(外來語), for the words imported from the rest of the world.