Why are spanish people referred to as "Latino"?

I often hear Spanish people referred to as "Latino" or from "Latin America". This makes no sense to me, since "Latin" is the basis for all romance languages, i.e French, Italian, Spanish, Portugese, etc, not just Spanish alone. "Latin America" doesn't really exist, since the areas that adopted the Spanish language were colonized and explored by Spain or Portugal (i.e modern day Brazil), so I think that should be called "Mes of Land formerly colonized by Spain or Portugal". My overall question is, why has "Latin" come to represent only Spanish people?