Romanian "sâmbătă" is like French samedi, German Samstag, Spanish Sabado, Italian Sabato -- from Hebrew Shabbat ("rest") by way of the Greek and Latin. In English it's "Sabbath," though in English the weekday is called Saturday (Saturn's day). (The ancient Sabbath day of the Jewish people is the seventh day of the week, Saturday.)
Romanian "duminică" is from Latin "Dominica," the Lord's Day, the traditional Christian designation for Sunday, first day of the week, day of the Resurrection of the Lord Jesus Christ which took place on the day after the Jewish Sabbath. In Romance languages, the first day of the week is called by a name derived from "Dominica" due to those nations' Christian heritage.