What does duty free mean?

Duty free means the buyer does not have to pay tax. This also means the sellers don't have to pay tax to the government, but it does NOT necessarily mean the merchandise cost less, because the retailers can mark up the prices as much as they want. A lot of customers ASSUME the goods are cheaper because they are "duty free", not paying attention to the higher marked up prices.

No import duty assessed.

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tax free

In other words, its tax free. So when you buy a product from a duty free store they charge you for the price of the product but do not add on the prices of tax.

That means you don't have to pay tax.