Still, none of them compare to this other local spot (it's 20 minutes away from me but it's so worth it). They only have a few fairly pedestrian flavors (caramel, white chocolate, cinnamon, etc.) but their lattes are like velvet.
It's some combination of two factors, barista skill and ingredients.
Barista skill: At all coffee shops your mileage will vary on drinks due to the baristas. For a latte, the foaming process isn't too hard, but it does require attention to detail. If a barista doesn't practice and taste for feedback they probably won't learn how to make the creamy foam you're talking about. Your small time shop is probably training their baristas in latte art, which is a symbol of proper latte foam creation, which the velvety texture your describing sounds right. I'm not going to describe the process, you can find it easily all over coffee websites, but at Starbucks I don't tend to see a barista even look like they're attempting to properly create latte milk/foam. They just heat the milk, take what foam gets created, and move on.
Look at the secret menu discussion, the focus is on them learning to make fancy sweet drinks, not become skilled at coffee drinks. Look at Kotowboy's dismissal of a con panna, that's ridiculous from a fine coffee standpoint, but at a sweet creations location it is a bit of a misplaced drink. My original post for con panna was partially a tongue-in-cheek jab at Starbucks, since it's a classic espresso drink that is often on the regular menu for coffee shop focused on Italian style cafe. Starbucks doesn't list it anywhere I know of (apparently his store does). Cafe machiatto (traditional or real machiatto) is on their secret menu, too, but don't order it, every Starbucks I've ordered it at the barista can't seem to grasp I don't want a sizable amount of milk poured in. Part of that is they don't know how to properly foam milk to even make a nice macchiato, that's why I tend towards con panna if I end up at Starbucks.
Ingredients: Starbucks is all about syrup. Your local shop may be, too, I don't know, but syrup thins out drinks built on foamed milk. Caramel is a great example, and a salted caramel mocha is an easy, fancy drink to make better than Starbucks at home. One reason is you can use caramel sauce and a chocolate powder/sauce. Even if you totally screw up the latte foaming process and make a bad espresso pull, the flavoring ingredients will create a great, thick texture and cover up all your faults. Watch your small shop, they may be using homemade ingredients or avoiding syrup, which can give your drink that thickness. Because they have limited options, this could very well be the case. Syrups give a ton of options for near free, but getting closer to using the raw flavoring takes more and more work for the baristas to learn the menu.