thanks faldage..

the first link is the type hat i wanted a name for.. (in a PM some one explained the common name for the was a rude word for part of female anatomy (send me a PM if you can't figure it out)-- fore and aft is OK, but i think i will end up calling a hat i am making in the same style a
A Pleated Kitty.. (or perhaps an other cat nick name.)
(hint there about the common military name.. (think of a part of female anatomy that has a cat name.. and then think of the rudest, crudest name attached to that part of the anatomy)

the second link, is what i know to properly be called a campaign hat, but more commonly called a smokey.. (just as the state troopers, who often wear just such hats (NY state troopers do) are called 'Smokey(s)'-- (they patrol state (not interstate) highways, and NY has lots of them!)

but i have love all the names, and i love some of the alternate names for pill box type hats (i only know fez, which is a specific (well to me!) type of pill box hat.

i think, the difference between a beret and tam is the fabric/construction. . Berets are made from felted wool (knit to shape, and then felted,) and tam's are made from fabric cut into a circle, or shapped from wedges sewn into a circle, the underside of the hat is made with another fabric cut into a donut like shape. (with a slit for a drawsting to fit the hat)

tams might well have tufts/pompoms, but berets often have stems..(small bits that stick up from the center)