The difference between a core competence and a distinctive competence is that:

a core competence is a competitively and strategically relevant activity that a firm performs well compared to its other activities, whereas a distinctive competence is a competitively relevant activity a firm performs well compared to other rival firms

a core competence usually resides in a company's base of intellectual capital, whereas a distinctive competence stems from the superiority of a company's physical and tangible assets

a distinctive competence refers to a company's strongest resource or competitive capability, while a core competence refers to a company's lowest$-$cost and most efficiently executed value$-$chain activity.

a core competence represents a resource strength, whereas a distinctive competence is achieved by having more resource strengths than rival companies.