Two-subtype model is variously cast as dominant / second function, inert / contact, accepting / producing, with the difference between terminologies coming down to preference. These subtypes are thought to reflect something innate and unchanging, not unlike the basic type. It is not clear what the real differences are between the two subtypes, but they are useful for diagnosis of types because otherwise it wouldn't be clear how such outwardly different people come to be categorized under one label.
DCNH is an entirely separate theory, with the subtypes being subject to change over the course of a person's life. Such changes are infrequent, so DCNH tends to remain stable over long periods of time. EII-contact can present in any DCNH type, as can EII-inert (no correlation).
EII-contact has a tendency to want to tell stories, relate various phenomena, and explain things about the broader world to others. Often has a stocky build, may gesticulate in conversation. EII-inert is less interested in sharing, more mindful of responsibilities. Will present everything in a way that accommodates his interlocutor to the greatest extent possible. More smooth and elegant movements.