When a US-based retailer sells to the US customer, they may be required to collect sales tax - in this case they only collect sales tax for orders shipped to New Jersey, probably because that's where they are located.
When a product is shipped to a different country, the customs in that country collect the local taxes and duties. Duties are tariffs (extra charges) imposed on the objects of different kinds at different rates.
When you buy duty-free at the airport for taking with you out of the country, the stuff you buy is not subject to local taxes, duties, etc. However, when you bring it with you to the country of your destination, you have to declare it, and there is a potential that if you bring too much with you, you will be charged duties. Canadians bringing alcohol/tobacco from the US know well how this works.
If you were to bring with you a piece of electronic equipment (e.g. a keyboard), your country (UK) may require a proof that you did not buy it abroad during this trip. If you do not have such a proof, they may charge us duties and taxes. Although this has gotten more lax in recent days with everyone carrying portable computers, but still, the burden of proof is on you.
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Regards,
Alex