You confused yet, Rainliberty?
Understand, please, that we are not dumping on you. But as Pete tried to point out, although a home-cook can, maybe, get away with confusing cuisines you're going to be a professional. And, as such, it behooves you to be as correct as possible. And in that regard your post is ambiguous.
I'm curious as to exactly what your professor said that sparket the discussion.
With the proviso that there are numerous regional variations, in general, if you say "Spanish," you mean food that represents the cuisines of Spain. "Spanish," other than as a language, has little relationship to Latino or Hispanic foods. In fact, because of the commonality of language, the same word is often used to describe radically different dishes. F'rinstance, a Mexican tortilla is a flatbread. But a Spanish tortilla is an omelete-like dish (well, more like a fritatta than a classic omelete.)
"Latino" and "Hispanic" are generally used interchangeably to describe the vast region of Central and South America. Although there is no hard and fast rule, the Carribean, even though there are hispanic roots, is mostly considered as a separate region, because there are vast culinary influences that never, or hardly ever, touched the mainland. And specialized ingredients as well.
But you're really better off looking at specific countries when trying to focus in on a cuisine. For instance, while the countries of South America have much in common, they have much more that is unique to them---even before you start looking at regional differences within each country. So you might want to develop the habit of saying, "Brazilian," food, or "Argentinian," than saying Latino or South American.
Here endeth the sermon.
In terms of Mexican, per se, there really is a difference between most Mexican food and Tex-Mex food. You could almost think of Tex-Mex as being its own regional Mexican food.
Most Americans probably use "Mexican" and "Tex-Mex" as synonyms. The result is that, unless you have a Little Mexico in your town, any "Mexican" restaurant is most likely to cater to that viewpoint, and it's menu will reflect it.