Duty free items usually mean goods that are sold to you in a foreign country, which have entered that country without local import taxes attached. This, however, can only be done from airport or ‘in-bond’ stores where the goods are then put into warehouses and not sold to the local population.
Duty free goods on cruise ships are legal because they are not sold to the people who live within the destination being visited. Also many cruise ships will close their shops whilst the ship is in port to abide by the local custom laws.
It’s important to note that many land-based shops often use the term ‘duty free’ to describe products that are discounted, as well as actual duty free items.
Tax free is a little different. In the Caribbean you do not pay VAT as you do in Europe, and you also don’t pay sales tax as in the USA. Therefore, if prices on certain items in the Caribbean have 30% off the prices you would usually pay, you are really getting 38% off because of the additional sales tax savings.