A national language is a matter of national identity. It differs from an official language, which is used for political and legal discourse.
Examples of national languages that are not official languages are Basque, Cherokee, Navajo (and other living Native American languages), Tibetan, and Irish.
Many national languages have been granted official recognition, if only to a limited degree. The Irish language, for example, is heavily subsidized by the Irish government, and used for special legal and governmental purposes (though not to a functionally meaningful degree), despite the fact that it is spoken by only a small fraction of the population.
