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Trinitarian formula. Is that the "Go ye therefore and teach all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Ghost." (Matt. 28:19)?

How does that square exactly with "Then Peter said unto them, Repent, and be baptized everyone of you in the name of Jesus Christ for the remission of sins, and ye shall receive the gift of the Holy Ghost." (Acts 2:38).

Are these two different baptisms?

No. Which is why Christ built a Church and gave it authority to lose and to bind. When there are seeming discrepancies in scripture, we need the Church to pass on the proper understanding.

"Bear in mind that our Lord's patience means salvation, just as our dear brother Paul also wrote you with the wisdom that God gave him. He writes the same way in all his letters, speaking in them of these matters. His letters contain some things that are hard to understand, which ignorant and unstable people distort, as they do the other Scriptures, to their own destruction. Therefore, dear friends, since you already know this, be on your guard so that you may not be carried away by the error of lawless men and fall from your secure position."
--2 Peter 3:15-17

Lots of lawless men and errors these days. Thank the Lord He built a Church to guide us, and didn't leave us to our own personal fallible interpretations of scripture.