Companion: A Companion can most simply be seen as a really expensive prostitute. Companions can be male or female, but the TV show only displays female Companions. Companions are required to go to an academy where they are trained in the arts of sex, some self-defence training, to sense the motives of others and perhaps manipulate those motives as well as regular persuasion. They are connected to some form of network where customers sign up for a said Companion. Companions are high ranking in status, and in a sense can be seen as nobility.
*Examples of self-defence may be a poisonous lipstick as shown by Saffron in the TV show that knocks out the person she kisses.
*Inara from the TV series is a Companion.
*More information can be found here: Companion
Doctor: Doctors are pretty much the same as they are in current day.
*SimonTam from the TV series is a Doctor.
Captain: The Captain owns the ship, and basically acts as the 'head honcho.' Not always does the Captain have to pilot his ship, but it is typically his responsibility to be able to help do a little of all the tasks. That may mean a little bit of the defence of the ship from bandits, a little ship maintenence and a little piloting.
*MalcolmReynolds from the TV series is the Captain.
Bodyguard: Should be proficient in martial arts or marksmanship. Simple job- to guard the person they are suppossed to guard.
*JayneCobb from the TV series would be a good example of a bodyguard.
Psionic: These people have Psionic Abilities. They are usually rather mentally unstable, but can still function well enough in real life. They are highly wanted by the law if gone loose. Psionics have their skull opened up and their brain examined. Any psionics who are not part of Hands of Blue probably escaped from the Hands of Blue, and Hands of Blue wants all the escaped psionics back. Some powers a psionic would have would be some form of mind reading or to kill a person with their brain. As River from the TV show demonstrated, since psionics are mentally unstable they might not see the world as we see it. What may look like a pistol to us may look like a stick on the ground to the psionic. They are very mysterious people.
*RiverTam from the TV series is a psionic.
Mechanic: Fixes stuff. On a ship, they are typically experienced with how the ship functions and knows more about the ship then just how to fix it.
*Kaylee from the TV series is a mechanic.
Pilot: Flies the said ship.
*Wash from the TV series is a pilot.
Bounty Hunter: Signs up to be hired for a bounty and hunts it, where hunt otherwise means take alive or dead. They do whatever they need to do to achieve their objective.
*JubalEarly from the TV series is a Bounty Hunter.
Shepherd: Preaches whatever religion to whatever person. A travelling priest.
*Book from the TV series is a Shepherd.