The best comparison I can think of is laptops: You certainly won't handle a gaming Alienware Notebook the same way you'd handle a Toshiba Ultralight. They're laptops, but designed for totally different day-to-day uses.
The same applies to folders (and bikes in general).
Unfortunately, in most cases, Montagues and Bike Fridays and Bromptons and Terns and so on don't have their own types. Most people simply refer to them as folders, then proceed to explain what kind.
If you were to divide them into categories, how would you do so? By weight? By use? By portability? By wheel-size? Or am I missing something?