Briefly, it works like this:
A VAT is a tx that is applied at each stage of the manufacturing and sales process. For example, when an item is sold to a store, the buyer is assessed a VAT, then when a customer buys the item, he is assessed another VAT. This is common in Europe and other countries. A VAT often replaces part or all of an income tax.
A sales tax is assessed only to the final buyer, not at the intermediate steps. It would s used in the U.S.