Competency is to do something successfully or efficiently. The person must have the necessary ability, knowledge, commitment and skills to do the task. These come from learning and regular practice.
Whereas the meaning of capability is the condition of having the capacity to do something.
What versus How
What, is the task at hand. Does the person have the capability for completing a particular task? For example: Leading a group of students in school for managing a sports event.
How, is the required skill and competency to do the task well.
The person does have the required skills and capability to execute the task as he is familiar with the requirements and the steps that need to be followed to reach the outcome. However, it is the ability to actually complete the task with a certain quality that will measure the competency of the person. So the person can lead a group of students to organize a school sports event (capability), but how that is done? what will the final outcome look like? etc is what will define the competency of the person.
I have come across teachers who have the capability but lack the competency to delivery their subject in class. The credentials are all there but the capacity to connect with the students (specially the ones who need more help) is lacking. Competency is also adaptability. How best can the teacher calibrate and use strategies from her repertoire to meet the students where they are. Adapt to meet their needs and then move them up.
there are students who have the capability to do a task but lack the competency to make it actionable. That means that the student has the potential that may or may not have been realized. But many times the teachers fail to recognize that and continue to promote the student who shows the competency to do it.
Competency increases over time with practice. So, give every student a chance to practice.