Example. Let's say Country Widgetland has a VAT tax of 15% modeled after the European VAT tax. Manufacturer WidgetMaker's Product Y is its most popular product and is made up of 2 components that cost WidgetMaker $4 and $6 each + 15% VAT tax for a total cost of $10 plus $1.50 VAT tax. They then sell this product at retail for $20 plus a 15% VAT tax for a total of $23.00 ($20 + $3 VAT) which is the price on the shelf [$23]. However, they get a tax credit for the $1.50 in VAT tax they've already paid, hence the government of WidgetLand only receives $3 in VAT taxes, effectively making it a 15% sale tax to the end consumer. In essence, the consumer/end user paid the entire $3 VAT tax that was ultimately sent to the government.
Now let's take this same scenario but North Carolina who let's pretend has just raised their sales tax to 15% from 7-8%. WidgetMaker buys the two raw products for $4 and $6 for a total of $10 bucks and pays no sales taxes. It then sells the product at retail for $20 and collects a 15% sales tax for a total consumer price of $23, including $3 in total taxes remitted to the state of NC, which is identical to the total amount remitted to WidgetLand.
In both cases it's a sale tax. The fact that US states don't require the price on the shelf to include the tax while the European government does is irrelevant to whether its called a VAT, a sales tax or other.
Your examples show you are not knowledgeable about taxes nor about VATs.
You have a simplistic view. Let’s leave it at that.