When I do the going plus infinitive, I say this is a present form the verb to go that relates to planning and I steer away from giving it a specific name. Suffice it to say for the learner that this is different from going and the object and that it is a way of stating that this used to state something has been planned. Way back when, I used to see an explanation of its use as distinct from something that is intentional. Since then I have dropped this methodology apart from the fact that the foreign student has difficulty to see the distinction between what is planned and what is intended. The new speaker usually confuses this with the present progressive by saying "I am going" plus the object. The way to get around the problem is to give distinctive cases where one is used and not the other.
The present progressive is used to talk about the now or something that is going to happen in the near future. If the person says he is going home he could be saying that he is leaving at the moment. He may be stopped along his route and after being asked the same thing, can answer in the same way. All this is very different from using going plus an infinitive and then the object. So if someone were to say I am going to go home, this means he has the intention of going home or is planning to do that. That may be modified by an adjective of time like later, to substantiate when the person has planned the action.
