Most people define the top hat and stovepipe hat as the same thing. In reality, there are slight differences between the two. Both hats have a similar design and even designers, as well as historians, talk about the hats as if they are the same. The hats were popular in the 19th and early 20th Centuries, but Abraham Lincoln made the stovepipe hat popular, according to most historical accounts.
Height
While both hats are tall, the stovepipe hat's cylinder was taller. The stovepipe hat looks more like chimney pipe, then the top hat. The height of the top hat is considerably smaller than a stovepipe hat, but no specific height is designated for either type of hat.
Crown
The crown is another difference between the top hat and stovepipe hat. Even though both hats have a flat crown, the way the cylinder runs into the crown is different. A top hat is flared at the tip where it connects to the crown. The cylinder of the top hat is wider at the top than it is at the bottom. The stovepipe hat is straight. The bottom of the cylinder is the same diameter at the top.
Formal Wear
Both hats get worn formally, but the top hat is considered more elegant than a stovepipe hat. You will see the top hat worn with tuxedos or for business affairs, while the stovepipe hat is commonly worn with a suit or even work attire.
Brim
The brim on the top hat is turned up, while the stovepipe hat has a flatter brim. For example, Abraham Lincoln's stovepipe hat had a flat brim and was wider than the common top hat.
History
The history of the top hat dates back to its introduction by the English hat maker John Hetherington. According to some newspaper reports, the hat scared many people in London when Hethertington first wore the hat publicly. The stovepipe hat, like Abraham Lincoln wore, was manufactured in the United States. It is said that Lincoln's hat was designed and made by a hat maker in Illinois, because the design and height was different than the top hat.