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.
Valencian Community
Spanish (Castilian or "castellano") has official status in all of Spain, including the Valencian Community. Aside from it, the Statute of Autonomy recognizes Valencian as the language proper to the Valencian people ("llengua pròpia"), and commends its protection and regulation to the Acadèmia Valenciana de la Llengua (AVL) under the Generalitat Valenciana. Valencian is also official in the autonomous communities of Catalonia and the Balearic Islands, where it is called Catalan.