What is the difference between a free trade agreement and a preferential trade agreement? What is the difference between a free trade agreement and a preferential trade agreement? 

What is the difference between a free trade area and a free trade agreement?
A free trade agreement stipulates free (cero tariff) trade between countries/states. In practice, this also includes broader provisions, such as agreements on movement of capital, goods and people (such as NAFTA). A free trade agreement will also mostly include all or a large portion of goods. 

In contrast, a preferential trade agreement is much less broad covering preferential (i.e. low or lower other countries) tariffs for a set of products or services. A preferential trade agreement can also just be unilateral or for a particular amount of years, etc. 

A free trade area is an area inside a country or state where free-trade rules (in general, but depending on the country and circumstance) apply. These areas are intended mostly for the import and export of goods, and are useful for a country that imports a good as an input by which another good is produced, thus lowering tariff costs for the producers. 

A free trade agreement is, of course, not a physical place (see explanation above).

Further, I recommend simply wikipedia in this case...