In education, skills and competencies have distinct meanings.
A skill is the ability to perform tasks and solve problems. It may include proficiencies, doing something well, ability to carry out complex activities of job functions, and is a learned ability to bring about the desired results. There are different types of skills, for example cognitive skills (ideas), technical skills (things), and interpersonal skills (people), to name a few.
A competency is more than just knowledge or skills. It involves the ability to meet complex demands, by drawing on and mobilizing psychosocial resources (including skills and attitudes) in a particular context. For example, the ability to communicate effectively is a competence that may draw on an individual’s knowledge of language, practical IT skills and attitudes towards those with whom he or she is communicating.
The European Commission’s Cedefop glossary conceptualizes a competency as the ability to apply learning outcomes adequately in a defined context (education, work, personal or professional development). A competency is not limited to cognitive elements (involving the use of theory, concepts, or tacit knowledge); it also encompasses functional aspects (involving technical skills) as well as interpersonal attributes (e.g., social or organizational skills) and ethical values.
A competency is therefore a broader concept that may actually comprise skills (as well as attitudes, knowledge, etc.). Competencies are taught in the 21st Century context as seen here.