Since it is starch in hot water in both cases, I wonder why starchy pasta water is so prized over adding (trigger warning for Italians) warm water and cornstarch when tossing pasta.
Flavor, that is all. The water left over from boiled pasta tends to have the flavor of the pasta, and a salty flavor. If you season your pasta water with salt, and I always do, why not bring some of that flavor into the sauce you are preparing? Better than just tossing it all down the drain.
Does it really matter? No, not really. But, if you want to use some of that water for something, add your starch to it.
I think for a few reasons -
- it's being used to add a bit of "silkiness" and just a bit of body, but not a lot of thickening, so the pasta water has about the right consistency for that,
- as others have pointed out, the flavor, and
- Since #1 and #2 are taken care of, and you already are always going to have pasta water when making the pasta, the convenience of having it already there, with no additional or separate preparation needed.
I don't think there's anything particularly magical if you have the desire for adding cornstarch, there's just no particular reason for it, all things being equal.
The starch in the pasta water has cooked for some minutes which reduces its taste. If you add raw starch to the sauce at the same time as the pasta the dish will get a starchy taste.
You could add the starch to the sauce several minutes before the pasta and cook the taste off if the sauce can handle it.
You could add some starch to the pasta water to make it work. Or you cook some starch-water seperately.