What is today known as "Spanish" (español) is acutally "Castillian" (castellano), it was the language spoken in "El Reino de Castilla" (The Castillian Kingdom) that eventually took over all other kingdoms in Spain. The name "Spain" (España) covers an area that includes all the kingdoms taken by the Castillian Kingdom, since they wanted their language to be the official one, they decided to change its name to "Spanish" (español) and forbad any other language in the entire country (Spain). This caused 1) other languages to be spoken only at home, they developed in a obscure way for many years, and 2) when they were allowed again a few decades ago, peoples in other regions returned back to speaking openly what was their mother tongue and rejected completely the Castillian language. Today, some feel annoyed when the term "Spanish" is used since there is no such as thing as "the Spanish language spoken in all Spain", there is Castillian, that they were forced to speak, the language of the oppressors, but it is not their mother tongue. Some do not care about this, while others feel annoyed if they are spoken in Castillian and not their mother tongue, some refuse to speak it on the streets when they are spoken to in Spanish even when they could do it perfectly... of course, if foreigners speak to the in Spanish they will be forgiven since it is understandable that foreigners will be likely to know Castillian instead of Mallorquí, Euskera (also known as Vasco), or any of the forms of Català (catalán). Since the vast majority of Castillian speakers actually live outside Spain, Mostly in America, and for us, the term Spanish, makes perfect sense because it comes from what we call "Spain", we do not feel annoyed at calling this language Spanish, thus, what could be considered politically incorrect, is widely accepted by most speakers of the language. Though, there are many, even in America, that insist on calling it Castillian, not Spanish.

Es una buena e interesante pregunta. De acuerdo a la Real Academia de la Lengua (el organismo oficial), ambos son correctos y el mismo idioma. Castellano es la lengua de Castilla, a diferencia de las lenguas de Cataluña y el País Vasco (Euskadi). Sin embargo, dado que es la lengua oficial del Reino de España, es llamada también español. Yo soy de Chile, y ambos nombres se usan casi indistintamente. Cuando era niño, en la escuela teníamos una clase de "Castellano", pero ahora se llama simplemente "Lenguaje" (clase de lectura, escritura, gramática y literatura castellana/española). Creo que en España prefieren usar español. Saludos, Daniel.