response to barachu vs candles, in bringing shabbat in early?

Question

I understand how it can be that lighting candles bring in shabbat.

But I don't understand how responding to Barachu(or any part of the davening) can bring in or be used to bring in shabbat.

I can only understand how it can work if it's only the candles that can bring it in.

If it's the candles that bring it in early, and responding to barachu that bring it in early, then the candles have to be done first, because if responding to barachu is done first, then shabbat is in and you can't light the candles.

And if responding to barachu is only ever done after the candles are lit and thus once shabbat is in, then how can responding to barachu bring in shabbat, (shabbat is already in from the candles),

I have a vague recollection once of somebody jumping up and saying not to say Barachu yet. I wonder if they said that because if he said it too early then it'd be before some people had lit the candles and thus it'd cause breaking shabbat. That suggests that it has the power to bring in shabbat but shouldn't be used to do so.

The shulchan Aruch though seems to perhaps suggest it is being used to bring in shabbat.

Shulchan Aruch 261:4

After responding to Barechu, even though it is still daytime, one may not make an eyruv nor cover over hot foods, for one has thereby already accepted /the holiness of/ Shabbos upon himself. In our times, reciting Mizmor Shir Le- Yom Ha-Shabbos 2* has the same effect as had the response to Barechu /in earlier generations/.

Answer 1

See the notes below which show that one can stipulate that lighting the candles will not bring in the Shabbas until later, while saying maarive absolutely does so.

DinOnline says

Driving After Lighting Candles 19 Av 5771 The Question:

Can a single person light shabbos candles with a bracha with a tanai (condition) that shabbos will be accepted later so that the person can drive to shul?

Answer:

Yes, this is permitted.

Only with regard to women, and with regard to a reagular situation, do we assume that lighting candles implies bringing in Shabbos, and it is therefore forbidden to perform labor after lighting candles.

However, with regard to men, no such assumption is made. Even for women, if a condition is made, the lady in question can light candles with a berachah, and stipulate that she doesn’t mean to bring in Shabbos until later.

Chabad

I'd like to add two notes:

a) Though lighting candles doesn't constitute an acceptance of Shabbat (for men, and for women who have in mind not to accept Shabbat at the time), the recitation of the Friday night Shabbat prayers (which also may be done before sunset, see More on Plag Hamincha) does constitute an absolute acceptance of Shabbat.2

b) We are required to "add" on to Shabbat, both when it enters and when it departs. This means that we may not do work until the moment of sunset (or the moment that three stars appear on Saturday night), but we must accept the holiness of Shabbat at least a few moments beforehand.

Thanks to @barlop for finding the following reference

Shulchan Aruch 261:4

4 After (28) responding to Barechu, even though (29) it is still daytime, (30) one may not make an eyruv nor cover over hot foods, for one has thereby already accepted /the holiness of/ Shabbos upon himself. In our times, reciting Mizmor Shir Le-Yom Ha- Shabbos 2* has the same effect (31) as had the response to Barechu /in earlier generations/.

Mishnah Brurah on Shulchan Aruch 261:4

(31) As had the response to Barechu. For, most probably, since mention is made of Shabbos /in this Psalm/, it is the same as an acceptance of /the holiness of/ Shabbos. The M.A. writes: “But now the custom is to say Mizmor Shir, etc., and yet to perform all kinds of labors until Barechu [i.e., if it is still before beyn ha-shemashos]. ” The reason is that originally this was the manner in which they accepted upon themselves this custom /of saying Mizmor Shir, etc./ ; they did not intend it to be an acceptance of /the holiness of/ Shabbos. All this /held true/ at the time of the M.A. But today the custom in all our localities is that as soon as Mizmor Shir is said, the congregation accepts /the holiness of/ Shabbos upon themselves, and it is then forbidden to engage in any work even if there is still much time remaining in the day. [P.Mg. and D.Hach.] The Derech Chochmah writes that the same is true for localities where Lechah Dodi is customarily recited, which concludes “ Bo’i Chalah ” : 8 this constitutes a true acceptance of /the holiness of/ Shabbos. (See To.Sh.)