Honestly, there are many similarities between Mexican and Spanish people and that is why most people confuse the two. A glaring difference between the two is that, a Mexican is an inhabitant of Mexico while a Spanish is from Spain and Mexicans are not Americans, while Spaniard are Europeans. Although Spanish and Mexican speak the same Spanish language, there are noticeable difference in their accents.
If we are to use the difference in culture to different a Mexican and a Spanish, it might require a lot of works because most Spanish cultures have been mixed with Mexican's culture. As a result of this, many foods in Mexico in the past belong to the Spanish. However Mexican people do have their own food. The reason for so much similarities between Mexican and Spanish can be attributed to the invasion of Aztec by a small Spanish group led by Hernan Cortes.