可以3 has an activity bring about a benefit (游泳可以讓身體健康 — swimming does the body good); 可以2 has a rule or person grant leave to someone (你可以走 — you may go). The subject sorts them: an activity that confers good is 可以3, a person who is allowed is 可以2.
可以3 says doing the thing serves to reach a good outcome; 能 says the conditions make a thing possible at all. They overlap (游泳能讓身體健康 also works), but 可以3 frames the activity as good for the result, 能 as merely able to bring it about.
treating the activity as a permitted person: 游泳被可以讓身體健康 → 游泳可以讓身體更健康
negating with 沒: 抽菸沒可以讓你健康 → 抽菸不可以讓你健康(and the enabling reading shifts to a warning)
reaching for 會 (likelihood / skill): 運動會讓身體健康(means it is likely to) → 運動可以讓身體更健康(it serves to)
English 'can' covers ability, permission, and 'it can do you good' alike, so learners use one word for all three where Mandarin sorts the enabling-benefit reading (可以3) from skill (會) and bare possibility (能).