Long Knives and Short Knives may have a visual difference, but function very similarly during combat. They contain a high handling for fast attacks against enemies and preform light damage per hit, this can be useful against both sluggish and agile enemies at close quarters.
In real life, knives have various purposes. In general, they serve as tools, utensils, and weapons.
In regards to the Khukuri, Khukuri (or Kukri) is a Nepalese knife used both as a tool and a weapon. In real life, they serve as utility tools in traditions and are used by some militaries such as the Nepalese Army and India's Gorkha Regiments.
Rais uses a Short Simple Knife on Dr. Zere by stabbing him with it.
For the Mighty Khukuri, it is misspelled as "Mighty Khukri" in-game.
Oddly, both the Simple Knife and Exquisite Short Knife's variants introduced in The Following both share the same names of Extravagant Knife and Fabulous Knife.