These terms are sometimes used interchangeably, and they shouldn't. I've even heard Latinos/Hispanics/Spanish people use these words incorrectly. Do you know some example of when you did not hear these words used correctly?
These 3 terms mean something slightly different. Instead of boring you to death on a historical, long-winded conversation on the differences, let's get straight to the point.
People of Latin American origin or ancestry. This includes Brazil, but excludes Spain. This focuses more on geographic location, rather than the language used.
People of Spanish-speaking origin or ancestry. This includes Spain, but excludes Brazil. This focuses more on language used, rather than geographic location.
Someone who comes from Spain. It's also a language.
This video goes more into detail about the terms, and it also give some historical background. :)