A competency is an action which you can carry out in a competent manner, so:
1. Someone who is properly or sufficiently qualified; capable:
a competent accountant.
2. Adequate for the purpose:
a competent performance.
There is no difference in meaning between competencies and competences – which to use is down to personal preference.
A skill is the learned capacity to carry out agreed results often with the minimum use of time or energy. For example, you may have the skill to speak French or Swahili, you may be skilled in researching, you may have IT or writing skills.
Looking at the area of work, common examples include time management, teamwork, leadership and planning. There are also specific skills which would be useful only for a particular job e.g programming.
This is a skill learned, or developed, in one place (job, study, volunteering, student society, community) which can be used in – transferred to – another place. For example, if you’ve given regular presentations in seminars, you will have developed a skill which you could then utilise in a wide variety of roles and situations – from presenting proposals to potential clients and running training sessions, to pitching for funding and giving you confidence to present yourself well in front of new people.
You may have had a part time job whilst studying which could demonstrate to a potential employer your ability to plan your time and manage your workload. It could also be used as an example to show customer focus, the ability to work in a team or communication skills – it would all depend on how you explained your experience.