Tricorn is actually a 19th century term referring to what the 18th century would have called a cocked hat. One, two, or three sides can be cocked up in different proportions. What we traditionally think of as a "tricorn" today is what they would have called a mathematical style, all equal sides. It was rather conservative in it's style and was quickly falling out of fashion in the 1770s for less equal styles often worn tilted slightly on the head. None of these styles mean anything really, some are just more up on fashion, others perhaps more conservative. Sort of like the cut of jeans today.

The bicorne comes in in the 1790s, finding it's popularity in military dress throughout the 19th century. It too has a variety of proportions and ways to wear it which vary throughout the years, in some cases specific to uniform rules.