In Latin America the language is called "castellano" simply because the countries in America were colonized in name of Isabel of Castile (Castilla). At that time several languages were spoken in the Iberian Peninsula: Portuguese, Galician, Catalan, Aragonese, Castilian, and others. The Castilian language was the language spoken in the court of Castile and so it was the language used to colonize America as it was spoken by Queen Isabel, who financed the voyage. At that time Spanish was not really a language, mainly because the country known as Spain did not exist. There were several kingdoms: Castilla-León, Aragón, Navarra,.
In Spain people tend to use the word "español" to refer to the language because it is spoken in the whole country alongside the regional languages whilst in Latin America they still refer to the language as "castellano".
Therefore in Spanish schools, students study "Lengua Española" and in Latin American schools they study "Lengua Castellana". The language spoken in Latin America is full of variations when compared to the language spoken in Spain and while the "castellano" retain lots of old-fashioned words, the "español" does not use them anymore. We could say that the Spanish spoken in Latin America is richer in the sense that it still uses words that are not used in Spain anymore.
