The real name of the Spanish language is Castilian, as in Spain there are languages which are not Spanish/Castilian, namely Catalan/Valencian, Galician and Basque.
Actually, the Spanish spoken in Mexico is different than that spoken in Spain, which is sometimes referred to as "Castillian" .
On a side note, there is Parisian french and Quebecois.
Spanish. I'm pretty certain there aren't any radically different dialects in any different countries as opposed to Portuguese in Brazil vs Portugal.