To answer that question we have to go back to the origins of the language. Spanish comes from Latin, which arrived in the Iberian Peninsula around 2,000 years ago. As in many other Roman provinces, Latin became Vulgar Latin by adopting some of the vocabulary of the indigenous languages and later developed even further into the romance languages. For many reasons,  mainly political  and cultural ones, the dialect that was common in the north-central region of Spain, including Castile, spread throughout the region. King Alfonso X helped the process by making this dialect standard for educated use of language and government administration. That’s where the term Castilian came from.

Castilian became the primary language of what is now known as Spain, after the country was unified under Christian rule in the 15th century, but it didn’t eliminate other Latin-based languages in the region like Galician and Catalan, or Euskera (Basque), a non-Latin-based language spoken in the Basque region. All these languages have coexisted in Spain ever since, with some regions being officially bilingual.

Today, the term “Castilian” is used to distinguish the north-central standard of Spanish from regional variations such as Andalusian (used in southern Spain). It is also used to distinguish between the official national language and the other languages spoken in Spain (Castilian vs. Catalan). Sometimes, not altogether accurately, it is used to distinguish the Spanish of Spain from that of Latin America and sometimes it’s used solely as a synonym for Spanish, referring to the “pure” Spanish promulgated by La Real Academia Española, which preferred the term “castellano” in its dictionaries until the 1920s.

In many parts of Latin America, the Spanish language is known routinely as “castellano” rather than “español”, whereas in Spain choosing terms – castellano or español – may have political implications, since some people from bilingual regions can be quite sensitive to the choice of term.

To sum up, both terms are equally appropriate to refer to the Spanish language, and are interchangeable except in cases where a contrasting reference is needed.