1. Technically, a Mongolian is a citizen of Mongolia, whether be of
Mongol, Russian,
Turkic, Chinese or any other ethnicity. Not to be confused with a Mongol. A Mongol is a person who is of Mongol descent. A Mongol can also be a person who's ancestor was a part of the
Mongol Empire. Roughly about 85% of
Mongolians (i.e citizens of Mongolia) are
Mongols. While most Mongols are Mongolians, not all Mongolians are Mongols. It is very common that these two terms are often used interchangeably by most people in the west and even by the Mongolians themselves. But nobody seems to notice and gives a crap about it.
2. A language spoken by ethnic Mongols in Mongolia, northern China, southern Russia and some parts of Turkic world. It is the main language of Mongolic language family which, along with Turkic and Tungusic languages, belongs to a much broader
Altaic language family that is spoken throughout Eurasia.
3. And anything (items, places etc) from Mongolia, I couldn't be bothered to write down, since it's too obvious.