I would say that there are three general types of trade barriers (methods of restricting trade between countries). These are quotas, tariffs, and regulations.
A quota is a law that limits the amount of a certain good that can be imported into a country. It says, for example, that only X number of cars can be imported into the US in a given year.
A tariff is a tax on imports. This raises the price of the imported good and makes it relatively more appealing to buy domestic goods.
Regulations are rules about the imports themselves. They are not supposed to be made with the purpose of restricting trade, but they often are. An example of this would be South Korean rules about beef. These are supposedly meant to prevent mad cow disease but are mostly used for limiting imports of US beef. So these are rules that are ostensibly not about trade but they end up being used to restrict trade.