halacha - Biblical vs. Rabbinical end of Shabbat

This question states, "havdalah ends shabbat (for one who didn't daven ma'ariv)." But won't Shabbat end on its own at some point--specifically, at nightfall--even if we don't make havdalah nor daven maariv?

I understand that melachos might still be rabbinically prohibited until we have made havdalah or maariv, because we are rabbinically required to usher out the Shabbat ourselves. But is it correct that the "Biblical" end of Shabbat--and therefore the end of Biblical prohibitions on melachos--comes automatically at nightfall?