Kiddush And Havdalah

In an earlier post it was cited the Rambam holds that kiddush and havdalah are the same yesod to honor Shabbos when it starts and when it ends.  Other Rishonim disagree and hold that havdalah signifies that it is now chol.  What is behind this machlokes?  

The Rambam in Laws of Shabbos (29:1) defines kiddush as  זָכְרֵהוּ זְכִירַת שֶׁבַח וְקִדּוּשׁ, a commandment to praise and mention the holiness of the day.  The Rashba in a Teshuva volume 4 (#295) says a similar construct.  However, the Ramban in Yisro (20:8) defines kiddush as sanctifying the day just like Beit Din sanctifies yoval.  [Even though Shabbos is kadosh by itself it is like a bechor animal where there is a mitzvah to designate it as kadosh even though it happens by itself as the Rambam rules in the Laws of Bechor (1:4).]  According to the Rambam we understand that kiddush and havdalah have the same function to praise Shabbos and they are the same mitzvah (see Minchas Chinuch (31:1) compares kiddush and havdalah to krias shema of the morning and evening.)  Hence, havdalah is also a law to praise the day of Shabbos.  However, according to the Ramban that the mitzvah of kiddush is to infuse kedusha into the day, that is only applicable by kiddush, not by havdalah and we must say that havdalah is a different din, not the same mitzvah as kiddush.  We don't find a concept to merely praise the Shabbos and in his view havdalah would be a form of accepting the chol.  That is why the Rambam holds kiddush can be done before Shabbos, as one is approaching the Shabbos, because then it is appropriate to praise Shabbos.  However, if one is sanctifying the day, it must be in a time when one is a timeframe of kedushat shabbos and that is why Tosfos holds that kiddush can be done on Friday afternoon only because tosefes Shabbos allows one to extend the kedusha of Shabbos.  Only when there is kedushat Shabbos can kiddush be recited.  

Another point on havdalah done on Shabbos.   The Mishba Berurah (299:1) brings the Magen Avrahom holds if one davened maariv of motzei Shabbos early on Shabbos, it is prohibited to eat until one says havdalah.  The Shaar Hatzion brings the Pri Migadim disagrees because when davening maariv early on Shabbos its still Shabbos and the obligation of havdalah doesn't kick in yet.  He obviously understands this is no concept of the dinim of chol extending into Shabbos not like the Behag mentioned earlier this week.