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.
Language border
For example, Spanish is spoken in most Central American and South American countries, but also in Spain. There are subtle but recognizable differences between the dialects, but there are different dialects even within the country of Spain. In many cultures there are still subtle differences between the terminology (called the register) used when talking to your boss and talking to your mother or talking to your friends. So where are the language borders?