A customary implication rests on an association well understood in ordinary social life: an open door may suggest hospitality, and being open-handed generosity. Such associations are conventions, not universal laws that admit no exceptions.
A rational implication has a more inferential connection between the stated matter and what is meant by it. Both require evidence that the speaker intends the indirect meaning.
Consider the expression “a hard hand.” In one setting it may connote stern control; in a medical conversation it could describe a physical condition. Neither reading is licensed by the words in isolation. Topic, audience, idiom and context determine whether an implication is present.