Your question Simcha613 is very well founded & taken.
To me Shabbos nite is from sunset/nitefall on a Friday until Alos haShachar on a Saturday morning. REason:- Because this is the nite as abstain from Melocho, as per the 4th commandment in the Torah.
Saturday nite thru Sunday morning, by definition is Leil Rishon, or Motzei Shabbos, but certainly is not Shabbos nite, because on that nite I perform Melocho all the way from lighting & extinguishing a Havdolo candle + a lot more.
Even this Saturday nite I shall be performing Melocho when I light my Yaknehaz lite, and then Saturday nite 7 weeks later, I shall also be performing Melocho, when I light my Yaknehaz lite & then carry my Tikkun Leil Shovu’os on Broadway [A Reshus hoRabim miDeOraisso] to Shul.