They are different!
Tax free shopping is the phenomenon in that tourists are able to shop at stores within a country, pay the full price (including VAT), and then receive a refund of the VAT amount when leaving the country to return home.
Duty free is specifically the shopping that occurs (generally) after security check-in at the airport where stores are offering a discount (duty free) for tourists.
Which is better?
Well - this depends on who you ask, but generally speaking, with tax free, you are able to shop at nearly every store in the country, but duty free has a limited selection of goods to buy.