I turned to the authority--Wickipedia and looked up both tams and berets. A tam (tam o'shanter) is a specific type of beret. It is named after Tam O'Shanter the hero of a poem by Robert Burns. It is brimless cap made of wool (most of the pictures I saw were wool fabric) with a toorie (pom pom) in the center. And indeed Mack is right-- the pom pom is the biggest distinction between a tam and a beret. Tams are (or were) generally worn by men and part of the headgear of Scottish soldiers. This style of hat when worn by a woman is called a tammy.
Now that we have discussed the tam, let's go into a little more detail on berets. A beret can be made of wool, either woven or knit, and often felted. This type of hat has been worn in Europe since the bronze age. It is also worn by many military units and these generally have a headband. Many European countries have traditions and specific types of berets associated with them.
Other types of hats are:
cloche--received its name because of its bell shape. A cloche is a felt (or knitted) hat designed to fit close to the head, down low on the forehead. The eyes of the wearer should be visible only slightly below the brim. The Eton crop, a short slicked down style, was inspired by the cloche.
tuque--a head hugging cap often referred to as a beanie in the U.S and a skully in other countries. (Skully sure gives you the impression of a tight fitting sort of hat.)
toboggan--when I looked this style up, I kept coming up with information on the wooden sled. After some searching I found a definition for a knit hat--a close fitting woolen cap with a tassel. Apparently, whether a toboggan is a sled or a hat has a lot to do with where you live, but we won't go into that.
There are lots of pictures of each style of hat, but wouldn't it be more fun to come in and look at some of the patterns in books and magazines here at the store!