"How can I make pizza at home just like italian vendor's original pizza?"
Have a really powerful oven that can safely and consistently go up to 900F; use a pizza stone, use good dough, use fresh ingredients for the sauce, use good cheese and meats.
Big pizza chains have standardized their recipes, processes and equipments (ovens) so they will (not always) try to find the easiest way to prepare a pizza so that the staff training costs (and operational costs) stay as low as possible.
They will prepare "generic" pizzas, sometimes they are good, sometimes they are bad, it all depends on our personal taste.
Small pizza shop will have a more "relaxed" approach to making pizza, they will have a better hands-on on the recipes, process and equipments, maybe they invested in a wood burning oven or a gas oven or a high-performance electric oven.
For example, in the best situation , the small pizza box will make sauce with the freshest in-season tomatoes (and can/freeze for the rest of the year), will buy better cheese and other ingredients and prepare the pizza dough and adapt it to the day's temperature and humidity.
They will bake the pizza and check with their eyes and nose instead of a timer.