There is a bit of a controversy around this. And I don't say you are wrong. It's just that I personally consider that Castilian should not be used and does no longer exist. Here's why I think it like so:
Castilian originated as one of several Romance dialects in the Iberian Peninsula. It developed in the Kingdom of Castile during the Middle Ages, distinct from other regional languages like Catalan or Galician. With the unification of Spain, Castilian gained prominence, eventually evolving into modern Spanish. This was not merely a linguistic shift but also a result of political and cultural dynamics. The language we now call Spanish has absorbed influences from Arabic, indigenous languages of the Americas, and others, diverging significantly from its medieval Castilian origins. For this, Castilian has now disappeared, you just need to read how Castilian was written to see it has nothing to do with modern Spanish.
Today, Spanish is spoken by over 500 million people worldwide. In contrast, the Castilian region of Spain has a much smaller population (~3M). Referring to the language as Spanish acknowledges its extensive global presence and its modern version. Just as we refer to the language originating in Tuscany as Italian, not Tuscanian, calling the language from Castile 'Spanish' aligns with common linguistic naming conventions. Languages often take their names from the nations or cultural entities they are associated with, not their specific regions of origin.
Modern linguistic institutions, like the Real Academia Española, regard 'Castilian' and 'Spanish' as synonyms but recommend 'Spanish' for its inclusive and global character.
This is a nice and thoughtful post and I agree mostly. I'd like to add that my use of the word "Castilian" reflects my experience of usage of the term here in Barcelona (when speaking "Spanish", Catalan, and English). It's not a hard rule of course, but people are especially likely to refer to Castille over Hispania when distinguishing from other languages spoken historically within the country.
The term also usefully refers to the prestige dialect of Spanish, as might be spoken in Madrid. This is useful to distinguish from e.g. the "al-andalus" (Andalusian) spoken in the south which is more treated as a dialect than a separate language (though the distinction is of course fuzzy).
(On the other hand Barcelona in particular has a significant population of sudamericanos who will usually say "español", certainly that term is well used and understood.)
> Castilian (castellano), that is, Spanish, is the native language of the Castilians. Its origin is traditionally ascribed to an area south of the Cordillera Cantábrica, including the upper Ebro valley, in northern Spain, around the 8th and 9th centuries; however the first written standard was developed in the 13th century in the southern city of Toledo. It is descended from the Vulgar Latin of the Roman Empire, with Arabic influences, and perhaps Basque as well. During the Reconquista in the Middle Ages, it was brought to the south of Spain where it replaced the languages that were spoken in the former Moorish controlled zones, such as the local form of related Latin dialects now referred to as Mozarabic, and the Arabic that had been introduced by the Muslims. In this process Castilian absorbed many traits from these languages, some of which continue to be used today. Outside of Spain and a few Latin American countries, Castilian is now usually referred to as Spanish.
> In Spain and in some other parts of the Spanish-speaking world, Spanish is called not only español but also castellano (Castilian), the language from the Kingdom of Castile, contrasting it with other languages spoken in Spain such as Galician, Basque, Asturian, Catalan, Aragonese and Occitan.
> The Spanish Constitution of 1978 uses the term castellano to define the official language of the whole of Spain, in contrast to las demás lenguas españolas (lit. "the other Spanish languages").
It's the same language. I'm a Spaniard, so I know it well. Name it the way you'd like, it can be called Spanish, Español or Castellano everywhere from Mexico to Patagonia, and from The Canaries up to the Pyrenees.
"name it the way you'd like, it can be called Spanish" is a very different proposition to "[you should say] Spanish, Castilian does not exist [and you are wrong to use that name]", which was the angle of the poster who kicked all this off.
> from Mexico to Patagonia, and from The Canaries up to the Pyrenees.
Sounds a bit imperialistic?
Notwithstanding the tens of millions of native speakers of autochtone non-spanish languages in these territories: Mapuche (260K), Quechua (7.2M), Aymara (1.7M), Guaraní (6.1M), Wayuu (400K), Mayan (6M), Miskito (150K), Garifuna (120K), Nahuatl (1.7M), Mixtec (530K), Catalan (4.1M), Basque (750K), Galician (2.4M). Spanish is quickly eroding all of these, but they still exist! (And this only counts native speakers. The number of people who are fluent in Guarani or Catalan is certainly more than the double of that.)
https://www.merriam-webster.com/dictionary/Castilian