I’m not a barista, and I can’t 100% confirm how Starbucks do it compared to their ‘normal’ coffee in the States. But here in Australia the difference between a flat white, a latte, and a cappucino is primarily the treatment of the milk/foam. I’ve got an espresso machine at home that I make coffee for the missus on (I personally can’t drink coffee.)
When you froth the milk with the steam probe, it behaves quite differently depending upon how deep into the milk you have the end of the probe. For a cappucino you want it shallow to create a lot of hard foamy froth composed of lots of big bubbles. For the flat white and latte you want little froth, composed of small bubbles. To me as a rank amateur, making them at home there is not a lot of discernible difference between a latte and a flat white, but the flat white is mainly warmed milk with some small froth on top, while the latte I increase the ratio of foam to milk. An actual barista would probably shake their head at me about now, but that’s the way I do it at home.