Names given to the Spanish language
Formally speaking, the national language of Spain, the official Spanish language, is the Castilian language (as opposed to regional Spanish languages like Galician, Catalan, Asturleonese and Basque). As such both names, "español" and "castellano", have distinct and independent meanings that may be required for clarity in some specific contexts.
Generally speaking, though, both terms can be used to refer to the (national) Spanish language as a whole, with a preference for one over the other that depends on the context or the speaker's origin. "Castellano" (as well as "Castilian" in English) has another, more restricted, meaning, relating either to the old Romance language spoken in the Kingdom of Castile in the Middle Ages, predecessor of the modern Spanish language, or to the variety of Spanish nowadays spoken in the historical region of Castile, in central Spain.
Hispanic and Latino Americans
The Spanish dialects spoken in the United States differ depending on the country of origin of the person or the person's family heritage. However, generally, Spanish spoken in the Southwest is Mexican Spanish (or Chicano Spanish). An old, colonial variety of Spanish is spoken by descendants of the early Spanish colonists in New Mexico and Colorado, which is New Mexican Spanish. One of the major distinctions of New Mexican Spanish is its heavy use of colonial vocabulary and verb tenses that make New Mexican Spanish uniquely American amongst Spanish dialects. The Spanish spoken in Florida and in the Northeast is Caribbean Spanish and is heavily influenced by the Spanish of Cuba Dominican Republic and Puerto Rico. Canarian Spanish is the historic Spanish dialect spoken by the descendants of the earliest Spanish colonists beginning in the 18th century in Louisiana. Spanish spoken elsewhere throughout the country varies, although is generally Mexican Spanish.