The Spanish Constitution, in its third article, clearly states that "el castellano es la lengua oficial del Estado" - that is, "Castilian is the official language of the State" - and it imposes on all Spaniards "the duty to know it". Thus, officially, the language referred to in the Spanish state as "the common language" is called castellano.
In spite of this, many Spanish viewers watching the 2020 Oscars were not at all appreciative of the moment in the ceremony when the singer Gisela - who is, incidentally, Catalan - sang a couple of lines in a multi-lingual performance of the song Into the Unknown (from the movie Frozen II) along with artists who all sang a line or two in their own languages.
The problem was that the English-language title which appeared at the bottom of the screen to show the language that Gisela was singing (at 1m57s in the video below) said: Castilian. Among other reasons, the choice of denomination was to differentiate it from the section sung by Mexican singer Carmen Sarahí a few moments later (2m20s). That's when the "Spanish" label appeared.
Most of the song, then, was performed in English, but nine different singers sang very short extracts in their own languages: Japanese, Polish, Thai, German, Norwegian, Russian, Danish, as well as Castilian and Spanish - the only language included twice, in different "dialects".
When used with reference to the language, español and castellano are, in general terms, synonymous, but the latter tends to be applied more specifically to the variation of the language used in the Spanish state. In English, both terms exist as well, Spanish and Castilian, with close to the same distinctions. But it seems that the English-language use of the term Castilian to describe their language rubbed some people up the wrong way.
Translation:
"Well at the Oscars they performed the song from Frozen 2 in several different languages. Among them 'Castilian' and 'Spanish'."— Diego E. Barros
"Spanish and #castilian? Hahaha it's like saying English and #British, they are just dumb" — TheFrisbeeman
"Castilian? Give me a f'ing break... Now it turns out we're not Spanish, we're Castilians xD" - Elena from Spain
Meanwhile, as usual, a certain sector blamed the Catalan independence movement for what they considered to be an attack:
"This is the best evidence that the Cata-Nazis have managed to destroy Spain. We are now Castilian." — ExterminaComunismos