Got it, okay what method is better? Do they both produce the same product? Or are they both completely different methods that produce completely different beers?
Disclaimer: I've never done a sour mash, but have done plenty of reading on it. I've done several kettle sours.
I don't know that I can say one way is "better" than the other. I will say that, IMO, kettle souring is easier to do and less chance of off flavors. If a sour mash is done correctly, and with a little bit of luck, yes it's essentially the same beer as a kettle sour, i.e., single note lactic sourness.
With kettle souring, you mash as usual, vorlauf/lauter as usual, and when you have your kettle full of wort, you pitch your lactobacillus, seal it up, and let it sour.
With sour mashing, you perform your mash and then sour in the mash tun, with the grains, before sparging. Also, most people use grains for their source of lacto in sour mashing. IMO, because of this especially, sour mashing can be more problematic when it comes to off flavors from unwanted microbes.
But most people use a pure lacto source (either commercial strain, yogurt, or probiotic shots) for kettle souring, which can be much cleaner and easier to work with. Moreover, by using grain for lacto in sour mashing, you have to keep it in the optimal temp range (around 100). But probiotic shots (kettle souring) can sour just fine at room temp.
Bottom line: IMO, kettle souring is much easier, reliable, and consistent than sour mashing. And if you get some unwanted microbes from the grains in sour mashing, it's essentially done and you have to throw it out. For those reasons, I always preferred kettle souring over sour mashing.
Eventually though, once I had enough taps and equipment, I quit kettle souring altogether and just pitch lacto and sacc together and let it ride.