When Yom Tov begins on Motza'ei Shabbat, havdallah is included in the Yom Tov Kiddush. However, when Shabbat follows a Friday Yom Tov, there is no Havdallah included in the Friday night Kiddush.
Why is there this difference? The bracha in the Havdallah ends "Hamavdil ben Kodesh L'Kodesh" - "Who separates holy from holy". There certainly are two levels of holiness, here - Shabbat and Yom Tov. So, why not say the Havdallah?
I'm surmising that when "rising" in holiness, gong from Yom Tov to Shabbat, there is no need to mention havdallah. However, that rule is not evident. If that is the reason, please provide a source for that rule.