Beis HaBechirah

Why does the Rambam call the Laws of the Beis Hamikdash, Hilchos Beis Habechirah, why use the term Beis Habechirah when the Rambam always calls it Mikdash?  In fact the other laws he calls Kli Mikdash and he describes the mitzvah to nuild a Mikdash, not a Beis Habechirah?  The Rambam wants to highlight what is special about the Mikdash in Yerushalyim over the Mishkan Shilo etc?  The place of the Mishkan wasn't intrinsically special over any other palce, merely the Mishkan happened to be there a place for people to come to offer sacrifices.  The Beis Hamikdash is different.  It is the place 'אשר בחר ה, the place itself and the Mikdash built there have kedusha because Hashem desired this place.  It is the the chosen place, the Beis HaBechirah (based on Likutay Sichos volume 24 Reah sichah 1.)
With this idea we can also understand why in the דיינו of the הגדה it uses the term Beis Habechirah as well; why that term specifically?  Because we are explaining what's the big deal we are making about leaving Egypt if at the end of the day we are back in galus?  Because we were chosen and no matter what the circumstances, we remain with that eternal connection to Hashem.  That is reflected in the Beis Habechirah, the chosen place for the chosen people.  (Based upon Toras Menachem 5626 second night Pesach.)