Argentines and Uruguayans use the term 'castellano' to refer to Spanish. This is the word used in high school for the textbooks and cpourses to refer to Spanish properly spoken, much as Anglophones use the term "King's English".
At one time, castellano (Castillian, the version of the language spoken in Castilla and Le?n) was used in the same way in pre-Franco Spain, but Franco and those that supported him in the Civil War wanted the language to unite the country. Their slogan was 'Espa?a, una grande y libre' (Spain, one, great, and free) and the national language became known throughout Spain as espa?ol and the term castellano was discarded.
There are four languages spoken in Spain: espa?ol, (everyone speaks espa?ol nowadays), gallego (Galician, spoken in Galicia, the traditionally Celtic province directly N. of Portugal), Catal?n, or Catalonian, spoken in Catalu?a, Valencia and Andorra, and vasco or euskadi, a non-Romance language related to no other language on the planet, spoken in the Basque provinces. During the Civil War, the Republican side was in favor of greater autonomy for the regions, including linguistic autonomy.
In Barcelona, it is usual to hear people in the stores speaking Catal?n, and then speaking espa?ol with foreigners. People who decide to live in Catalu?a are expected to try to learn Catal?n, even though it is unnecessary in any practical sense.
In Buenos Aires, they use the word vos in lieu of usted or t?, and have a variety of local terms. There used to be a sort of Italian-Spanish patois called lunfardo spoken around the Boca area, but this is mostly a thing of the past. Argentines are extremely friendly folks, as are the Spanish. My experience is that if you speak the language, pretty much everyone is more friendly and outgoing to tourists than Americans, especially East Coast Americans.
There is less difference between regional versions of Spanish (Mexican, Chilean, Colombian, Argentine) than there is between Ile de France French and Quebe?ois French. Cubans have a whole lot of words that no one else uses, and they often do not recognize the standard words for a lot of common items.
There is only one official dialect of Spanish, called papamiento, spoken in the ABC islands of Aruba, Bonaire and Cura?ao (it contains words from Spanish, Portuguese, Dutch and English). There is another, unrecognized patois mixture of Spanish and English spoken in the Orange Walk and Corozal districts of Belize.