The phrase refers to the objective existence of distinct ethnic groups in a country; whereas multiculturalism refers to an official policy of acknowledging the equality of these distinct groups. A country may be, or may have been, multi-national but not multicultural.
Multinational states differ from states such as Iceland and South Korea in which an overwhelming majority of the population is ethnically homogeneous. China and India are the largest countries in the world by population and are both multinational, having many recognised ethnicities.