competence and competency

I see none.

I would say competence refers more generally to an ability to understand and think critically whereas competency is typically used when describing knowledge and understanding of specific area. e.g. "He has a demonstrated competency in applied physics" or "core competency" versus "he was determined to have been competent at the time of the murder." But it is often used interchangeably e.g. "a com

I would say one is a description of an attribute and one is the possession of it

In this case, context is everything. "How is either being used" is necessary to answer.