What is it called when a group of people identify themselves based on a distinct culture, belief system, religion, or history?

a. race

b. ethnicity

c. nationality

d. class

The correct answer is c: nationality.

Many countries are built around a nationality, for example Estonia and Finland. Others could be said multi-national for example India (although there is also an Indian nationality, but apart from this, people are also of "smaller" nationality: Marathi, Gujarati, etc)

Ethnicity is a similar word, but it necessarily involves a certain degree of (genetic) relation, which a nationality does not need to have.