Mandarin is the standard and official form of language for China, spoken by over 730 million people, the Chinese people would call it “Puton Hua”, while Chinese ie”Zhong Wen” is referring to China and the language spoken by Chinese people. Though China has rather a good number of languages spoken by its people, Chinese is referring to Mandarin, the standard and official language.
All that being said, we could say Mandarin = Chinese in this case. That’s the language you are learning from us.