There are several components that make up chemical propulsion systems. These can be divided into three major groups: The Propellant Delivery/Feed System, the Thrust Chamber Assembly, and sometimes Thrust Vector Control systems.
Each of these groups can be further broken down into specific components that make up the group, and often have dedicated branches or engineers who specialize just in those components.
Propellant Delivery/Feed System
Includes tanks, plumbing, valves, filters, and fluid management devices needed to ensure the propellant is adequately delivered to the rocket engine at the right conditions.
[link to CFM/LTF group]
Turbopump or Pressurization System Component
Includes turbomachinery/pumps or high-pressure gas delivery systems needed to help push the propellant from the tanks to the engine. These components fall under the broad category of propellant feed system.
Thrust Chamber Assembly
Contains the combustion chamber, injector, ignitor, cooling circuits and nozzle needed to produce the hot gases to produce thrust.
Thrust Vector Control System Component
Includes gimbals, controllers and actuators needed to move the engine around to help point it, so the thrust is going in the desired direction to move the rocket.