Question: Why was it considered accepting Shabbos by mistake in a case of a congregation that didn’t get a shofar until a few minutes before sunset and they had davened maariv early and they can blow the minimal amount of shofar blasts but once one lit Shabbos candles before lighting Chanukah candles by accident it is not considered a mistake and he cannot light candles anymore by himself?
A. The scenario of the shofar could be if Rosh HaShana was Thursday/Friday and the shul did not have a shofar. They sent someone to retrieve a shofar from a few towns over and he got delayed and was not showing up. Late Friday afternoon they essentially gave up and davened Kabbalah Shabbos and maariv early sometime between plag hamincha and sunset. Then the guy came with the shofar. The Mishna Berura (600:7) says that if there is no expert shofar blower who has not taken on Shabbos to blow then one who already accepted Shabbos can blow the minimal amount without a blessing. The Taz there says this is because they accepted Shabbos by mistake.
B. Accepting Shabbos early is essentially making a vow.
Answer: The answer is found in the Responsa Beis Shearim 3:93 in the name of his Rebbe, Rav Pearls who said that the difference is that the obligation for the mitzvah by shofar already existed when they brought in Shabbos and therefore accepting Shabbos was like a vow said by mistake which does not need to be disavowed. But there is no obligation of Chanukah candles until the night time so when she lit Shabbos candles she was not obligated in Chanukah candles yet, if so then even accepting Shabbos was like making a vow by mistake nevertheless it was a mistake that just materialized after the vow was made so it needs a special annulment with an excuse and regret in front of 3 or a sage therefore Rav Shlomo Zalman Auerbach adds that at that point it is better just to ask someone else to light for you. (See Dirshu footnote 5 here.)