In conclusion, security is the precondition of political freedom and political freedom is the prerequisite for economic freedom.
Do precondition and prerequisite mean the same in the above? Is there a difference?
They do appear to mean the same thing. With apologies for borrowing from the usage of
A precondition must be 'true' for the ensuing process, but may not be a process in itself. A prerequisite, on the other hand, is a process by itself that must have been achieved and completed before the next process starts.
In the example you cite, the precondition must be true but is not necessarily a completed process or it may have other co-requisite ingredients or conditions. The latter part of the sentence is definitely more definite.
Hoping that it makes some sense!
It is possible the speech writer /author just want to use a different word instead of repeating the same word. It may be a "distinction without a difference."