Free trade: the trade between three or more countries without the use of tariffs, quotas, or other restrictions. NAFTA, CETA and the TPP are examples of free trade.
Protectionism: the practice of protecting local or domestic industries foreign competition by taxing imports, imposing tariffs, providing domestic subsidies to exporters, and imposing non-tariff barriers which restrict imports.
Tariff: a tax or duty to be paid on a particular class of imports or exports. For example, company A produces yogurt in Greece and exports the yogurt, which costs $100 per pound to Canada. A 20% tariff would require Company A to pay the Canadian government $20 to export the yogurt here.
Quota: a restriction on the amount of a particular product, that under official trade agreements, can be produced, exported, or imported. For example the country has a quota that restricts oil production to 1 000 000 barrels of oil per day.