Here are several culinary stations and their responsibilities.  Demi sous chef was not listed in the source, but one would presume a "demi" sous chef has about half as much authority and responsibility. 
Chef de cuisine, executive chef and head chef
This person is in charge of all things related to the kitchen which usually includes menu creation; management of kitchen staff; ordering and purchasing of inventory; and plating design. Chef de cuisine is the traditional French term from which the English word chef is derived. Head chef is often used to designate someone with the same duties as an executive chef, but there is usually someone in charge of them, possibly making the larger executive decisions such as direction of menu, final authority in staff management decisions, etc. This is often the case for chefs with several restaurants.
Sous-chef
The Sous-Chef de Cuisine (under-chef of the kitchen) is the second in command and direct assistant of the Executive Chef. This person may be responsible for scheduling and substituting when the Executive Chef is off-duty and will also fill in for or assist the Chef de Partie (line cook) when needed. Smaller operations may not have a sous-chef, but larger operations may have several
 Expediter
The expediter (in French aboyeur) takes the orders from the dining room and organizes them on the tray, and a food runner will bring the food to the guest. This person also often puts the finishing touches on the dish before it goes to the dining room. In some operations this task may be done by either the executive chef or the sous-chef.
Chef de partie
A chef de partie, also known as a "station chef" or "line cook",[2] is in charge of a particular area of production. In large kitchens, each station chef might have several cooks and/or assistants. In most kitchens however, the station chef is the only worker in that department. Line cooks are often divided into a hierarchy of their own, starting with "first cook", then "second cook", and so on as needed.
Commis (Chef)
A commis is a basic chef in larger kitchens who works under a chef de partie to learn the station's responsibilities and operation.[3] This may be a chef who has recently completed formal culinary training or is still undergoing training.[4]