For the language:
* 汉语 (Hanyu) - This is the most common and neutral term, meaning "Han language".
* 中文 (Zhongwen) - This is another common term, meaning "Chinese characters".
* 华语 (Huayu) - This term is more commonly used in certain regions like Singapore and Malaysia, and means "Chinese language".
For the people/culture:
* 中国人 (Zhongguoren) - This means "Chinese people".
* 中华 (Zhonghua) - This refers to the Chinese nation or culture.
* 中国 (Zhongguo) - This is simply the name of the country, but can also be used to refer to the people or culture.
So, depending on what you want to say, you could use any of these terms.