دار or بيت?

In the discussion of Ḥajj the author of Hidāyah explains that a person going for Ḥajj can put on the Iḥrām prior to the Mawāqīṭ, he mentions regarding adoring the Iḥrām from the house.

The word دار (house) refers to a house with many rooms, whereas بيت (house) is smaller than the دار, generally referred to only a room. However in the discussion, to refer to the house of Allah the term بيت is used; بيت اللّه meaning, the house of Allah (Kaʿba). For this reason the author uses the Ism al-Tasgīr (اسم تصغير) for دار, to not decrease from the تعظيم [grandeur] of the house of Allah as it is mentioned with the word بيت.