It is my understanding that the booster is identical in every way, including dosage, as the initial vaccination.
I believe you are correct. The booster is no different than the first or second shot.
I read a column recently by an MD who clearly stated that to be the case.
All three shots are identical and the shots now are the same as the ones that they used at the very beginning.
The whole booster thing is smoke and mirrors. More language manipulation by the left.