Makes sense. The one on the left is probably particularly crap. Higher salt content, more skim milk % than better quality part-skim cheeses.
Like you said, you can get a lot of info from the feel. I think those cheaper cheeses really over salt early, and work the curds harder to expell as much whey as possible to get the cheapest product and longest shelf life. And they feel rock hard.
There is a store near me with a house brand LMPS mozz that has the opposite problem. It feels soft, but it doesn’t have the right pulled texture of real mozz. So it melts, but kinda in a puddle, and it breaks well before it browns.
The one on the right doesn’t say low moisture, but I think based on the nutritional information it would still be that. It’s the same calories/gram, fat, protein and salt as the 2 brands I use, and they are both marked low moisture. Maybe Walmart figures they’ve given low moisture cheese a bad reputation so they don’t want to call it out on the whole milk cheese package.