Thank you for your thoughtful question. The relevant Greek word in John 1:33 is "en," which is frequently rendered "in" but can also mean "with." Thus, we see disparity in the translations of this text. "

[Jesus] is he which baptizeth with [en] the holy spirit." The meaning is the same either way it is rendered. Baptism means immersion, so whether we read that Jesus immerses us "in" the holy spirit or "with" the holy spirit, the meaning is the same. The believer will be immersed into, or inundated with, the holy spirit.

The same word "en" is used in the companion text, Matthew 3:11. "I indeed baptize you with [en] water unto repentance, but he that cometh after me is mightier than I, whose shoes I am not worthy to bear: he shall baptize you with [en] the Holy Ghost, and with fire." The word "en" in both uses in this text refers to the medium that persons would be immersed into. (The "fire" in this case was the fire ending the Jewish Age, as Matthew 3:10 suggests. Believers would receive the holy spirit, the balance of the nation would experience the fiery judgments of the Roman campaign against Israel.)

The holy spirit is the medium into which believers are immersed. No text speaks of the holy spirit as anything like a "person" that accomplishes an act of baptism upon people. The holy spirit is simply as Ephesians 4:30 describes it, the spirit, or influence, or power, of God acting upon believers. Therefore, in answer to your question, John 1:33 is describing the same baptism into the body of Christ that 1 Corinthians 12:13 describes.