Internal taxes were the general taxes imposed on items and lands within a nation or colony. These are taxes on goods that most people need or use, and tended to affect most free people in the nation. Since these taxes were so widespread, they were typically decided and collected by the provinces of the nation themselves rather than the entire national government.
External taxes are taxes more oriented toward tariffs and export/import taxes levied against goods being shipping in (and out) of the nation. These taxes were limited in scope: they tended to take effect only in shipping towns, and only a select group of people, notably merchants, needed to pay them. The amount of the tax was generally carried into the price of the goods themselves and was not levied against the people who then bought the goods.
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The Stamp Act that England created against the American colonies is a good example of internal and external taxes. The Stamp Act levied a tax against people who bought nearly any paper products in the United States. Because these paper products were bought by everyone, and not just traded by merchants as imports, the tax affected all the colonies and was considered by many to be an internal tax. However, internal taxes were typically decided by local governments, not governments of distant nations, even if they owned the colonies in question.
While the Stamp Act created additional unrest that helped lead to the American Revolution, there was debate even in the American colonies as to what type of tax it was. Many taxes blurred the line between internal and external in some ways. The external tax may be applied to all those who bought imported goods instead of only the distributors, while internal taxes may be limited only to certain goods received at certain ports. This made it difficult for some to spot the difference.
Today, internal and external taxes are largely a thing of the past, mostly because government tax systems have become much more complicated. Import and export taxes are often levied on a case-by-case and nation-by-nation basis. Sales tax may be considered an internal tax because it is decided by each state instead of the federal government, but the term does not hold much meaning today.