How do Thai People Make Peanut Sauce?
Peanut butter is just ground roasted peanuts essentially.  The american style peanut butter tends to be sweetened, as well as having extra oil and salt.  But they are only slight flavour/texture enhancers (not that I think sugar enhances it, UK peanut butter is unsweetened usually).

Satay sauces are essentially just peanut butter sauces, roast some peanuts, grind them, then add to some lightly fried shallots and garlic, with chilli, soy sauce, lemon juice, salt, sugar and if you want it authentic probably some nam pla (fish sauce), or blachan (shrimp paste), all of the above to taste.  Thin with water and reduce to the consistency you desire.