The existing answer seemed confusing to me, so I thought I'd do some research and post an answer.
Distinguishing paragraphs of the article for me are:
The cuisine we now call Tex-Mex is rooted in the state's Tejano culture (Texans of Spanish or Mexican heritage who lived in Texas before it became a republic) and also Mexican immigrants who hailed largely from Northern Mexico. Until the 1970s, though, most people referred to it simply as Mexican food.
If you're looking to identify the distinguishing characteristics of Tex-Mex, enchiladas are a good case study. In the classic Tex-Mex version of cheese enchiladas, grated yellow cheese is wrapped in tortillas, and then covered in a dark red chili sauce mixed with ground beef. You'll also find other typical Tex-Mex ingredients like pinto beans and rice served on the side.
But Iliana de la Vega, the chef and owner of the Mexican restaurant El Naranjo in Austin, never ate cheese enchiladas while growing up in Mexico City. She recalls eating foods like chiles rellenos and salads composed of chayote or nopales. Beef was a bit of a rarity. "In traditional Mexican cooking, we eat a lot of chicken and a lot of pork," she explained. If they had enchiladas, they were usually smothered in a green tomatillo sauce or mole, and sprinkled with a white cheese. "My mother was from Oaxaca, so we had mole maybe twice or three times a month," she said.
Another difference is the abundant use of cumin in Tex-Mex cuisine. "We use it a lot in the north, but it's not a spice we use much in the southern part of Mexico," says de la Vega. Robb Walsh links the heavy use of cumin to the first wave of Canary Islanders who emigrated to San Antonio in the 1700s. Today it's still a key ingredient in chili con carne, along with chili powder, which, according to Walsh, is a uniquely Texan invention developed by a German immigrant in New Braunfels in the late 1890s. In the late 1800's, chili con carne was regularly ladled out at bargain prices in the streets of San Antonio at its famed chili stands. "Tex-Mex was never the cuisine of the upper echelon of society," Bayless observes. "It's a peasant, working class cuisine."
but Tex-Mex has been evolving too:
The Tex-Mex that most of us think of, full of Velveeta cheese and pre-made taco shells, was shaped by the development of convenience foods in the 1950s. That time period left Tex-Mex, and even Mexican food in general, with a reputation as "just a cheap cuisine, full of sour cream and processed cheese, and that everything is greasy," says de la Vega.
Summing up: Cheese enchiladas, chilli con carne, use of beef, and use of cumin, etc separate Tex-Mex from traditional Mexican.