Names given to the Spanish language
Formally speaking, the national language of Spain, the official Spanish language, is the Castilian language (as opposed to regional Spanish languages like Galician, Catalan, Asturleonese and Basque). As such both names, "español" and "castellano", have distinct and independent meanings that may be required for clarity in some specific contexts.
Generally speaking, though, both terms can be used to refer to the (national) Spanish language as a whole, with a preference for one over the other that depends on the context or the speaker's origin. "Castellano" (as well as "Castilian" in English) has another, more restricted, meaning, relating either to the old Romance language spoken in the Kingdom of Castile in the Middle Ages, predecessor of the modern Spanish language, or to the variety of Spanish nowadays spoken in the historical region of Castile, in central Spain.
Spanish language
Most Spanish speakers are in Hispanic America; of all countries with a majority of Spanish speakers, only Spain and Equatorial Guinea are outside the Americas. Nationally, Spanish is the official language—either "de facto" or "de jure"—of Argentina, Bolivia (co-official with Quechua, Aymara, Guarani, and 34 other languages), Chile, Colombia, Costa Rica, Cuba, Dominican Republic, Ecuador, El Salvador, Guatemala, Honduras, Mexico (co-official with 63 indigenous languages), Nicaragua, Panama, Paraguay (co-official with Guaraní), Peru (co-official with Quechua, Aymara, and "the other indigenous languages"), Puerto Rico (co-official with English), Uruguay, and Venezuela.
Spanish has no official recognition in the former British colony of Belize; however, per the 2000 census, it is spoken by 43% of the population. Mainly, it is spoken by the descendants of Hispanics who have been in the region since the seventeenth century; however, English is the official language.