No, Mongolians are not Chinese, ethnically. There are about 5 to 6 million ethnic Mongolians living in Southern Mongolia (which is geopolitically part of China) so it can add a bit to the confusion.
In Mongolian culture, it is offensive or considered rude to mix Mongolians with Chinese people, something that tourists should keep in mind.
The origins of Mongolian people are said to be from Siberia and Central Asian steppes. While there are about 10 million ethnic Mongolians in the world, the look of a Mongolian can vary depending on which tribe they are from and what kind of ancestry they have.
Some Mongolians can have red or yellow hair with green, blue or hazel eyes. While they are in the minority, some ethnic Mongolians have a small portion of European ancestry which are more present in Western part of Mongolia.