While I was having a coffee with my family in the rotating café in New York one guy asked us if we were from Spain. I told him we were from Argentina, and he commented 'but you speak Spanish... or Castilian' like hinting it was the correct form of the name. I answered 'yes, it's the same' to which he responded he thought we called latinamerican Spanish Castilian rather than Spanish. The concept took me by surprise, but the most astounding fact was that many people in Latinamerica actually think this. They think Castilian is a term used just for Latinamerica.
This is not so.
Actually there is no real 'Spanish' as such, if you take that to mean that all of the Kingdom of Spain has actually only one language, which is not so. When the kings of Castile unified the whole country under one ruling house they established the speech of the kingdom's capital as the standard for the kingdom's language, which happened to be the Castilian variety of Romance. This is the language the spanish brought with them to America, and it is the language spoken in most of the continent, with a great number of variants.
Spaniard Spanish is no less Castilian than American Spanish. If you take 'Spanish' to mean 'the official language of Spain', but actually Spain has many languages, most of them romance (Catalan, Galician, Aragonese, Leonese, and many more) or even isolates (Basque, and many different dialects and variants).
So at best you can either call Castilian to all forms of the Spanish which is official in Spain and used in all Hispano-american countries or call Spanish to all of its forms.
But the error does exist even in native speakers in the american continent. Another example of how Spanish tends to categorize and split and assign concrete meanings to all its words trying to turn all synonyms into different words for different concepts.