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.
Barcelona
Spanish is the most spoken language in Barcelona (according to the linguistic census held by the Government of Catalonia in 2013) and it is understood almost universally. After Spanish, the Catalan language is the second most spoken one in the city, and it is understood by 95% of the population, while 72.3% can speak it, 79% can read it, and 53% can write it, thanks to the language immersion educational system.