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.
Names given to the Spanish language
Spaniards tend to call the language "español" (Spanish) to contrast it to languages of other states, such as in a list with French ("francés"), German ("alemán"), etc. "Castellano" (Castilian) by contrast, is more often used when contrasting the language with other regional languages of Spain: official languages like Basque, Catalan and Galician or unofficial ones like Aragonese, Asturian, Extremaduran and Leonese. The Spanish Constitution of 1978 uses the term "el castellano" to define the official language of the whole State, opposed to "las demás lenguas españolas" ("the other Spanish languages"). Article 3 reads in part: