It sounds like you are curious as to why your homemade pizza doesn’t "string" like the pizzeria.

Most pre-bagged shredded mozzarella cheese at the supermarket is "part-skim", which means it doesn't contain a lot of milk fat, and therefore doesn’t "string" properly, whereas most pizzerias use "whole milk" mozzarella, unfortunately you can only usually find whole milk mozzarella in blocks, so you have to grate it yourself, but you'll find it not only strings, but tastes much better on your pizza.