Competency Mapping refers to creating a combination of technical, behavioural, and psychological skills required for a position. And, usually, these are almost always identical at a particular band or grade except for the technical details.
A Job Specification on the other hand is the brasstacks for a job. Usually, it will include core deliverables, expectations from the incumbent, working conditions, roles & responsibilities, immediate hierarchy etc...
Remember, the core difference between the two is this: Competency Mapping = Position and Job Specification = Each individual Job