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
Valencian ( or ; endonym: "valencià", "llengua valenciana", or "idioma valencià") is the traditional, historical and cultural linguistic variety of Catalan spoken in the Valencian Community, Spain. It's officially recognised as a language in the Statute of Autonomy of the Valencian Community signed in 1982 and approved by the Valencian regional government and the Spanish government. In the Valencian Community, Valencian is the traditional language and is co-official with Spanish. A standardized form exists, based on the Southern Valencian dialect.