Hispanic and Spanish are two words referring to different groups of people. Though the people they refer to and their meanings have changed over time, both words are still used prominently today. Hispanic originally referred to the people from Hispania or the Iberian Peninsula.
Spanish originally referred to anything from the country of Spain. Today, their meanings are different, with Hispanic referring to people who speak Spanish and the term is mainly referred to those in the United States.
Today Spanish has expanded to refer to the culture, food, and people from Spain. The origin of the words also differ. Hispanic's origin is Latin, and the word Spanish is originated from Spain.