I'd like to add a couple of things about buffallo mozzarella, one of my other food obsessions since I grew up not far from the various production areas.
In Italy, you will find subtle but detectable differences between the various production areas, Batipaglia for example on the Salerno part, and Aversa/Grazzanise etc. on the Caserta part, two comparable yet different animals.
In the States, we do not enjoy any of that. This topic has been discussed before but the main culprit IMHO is pasteurization. Under European law, mozzarella milk undergoes a process that is called thermization, a method for sanitizing raw milk with low heat that is useful for partial removing of pathogens, while keeping the good bacteria flora in (see Wikipedia). Buffalo mozzarella for US export undergoes pasteurization, which destroys most of the bacteria, the good and bad alike.
It matters to us pizzamakers especially for the following reason. One consequence of pasteurization is longer shelf life, up to 15-20 days, while Italian mozzarella needs to be consumed fresh (2 days max) and is best enjoyed if kept at room temperature, without refrigeration. When U.S. imported mozzarella stays in water for weeks at a time, it gets oversaturated with water and loses its characteristic texture. This makes the product even more watery that it would otherwise be.
When I buy buffalo mozzarella in the U.S., I always make sure that the batch has at least 10 days left on its expiration date, meaning that it has been approximately a week in water. Costco often times carries sequential batches, if you look in the back, you could find fresher mozzarella with almost 20 days of remaining shelf life. Longer expiration days translates in better texture and less water.