These terms are used liberally in management literature. In strict technical terms, skills involve using hands and feet, or can be learned through repeated practice such as playing a piano, a musical instrument, preparing Bonus Calculations, appointment letters, or training.
Competency, on the other hand, is behavioral, indicating an orientation towards issues like risk-taking, self-control, etc. It is important to note that these are managerial competencies. Competency is also used in the sense of possessing technical knowledge in a specific subject area like Accounting. This is often referred to as technical or functional competency.
In any case, best of luck for your interview. From my experience, most managers do not have a clear understanding of these terms and tend to use them loosely, so do not be disheartened if the interviewer provides their own unique definition. Reading and critical thinking are not always qualities found in managers, particularly HR managers in my experience.