They rowed across the Hudson River from New York to New Jersey in the early dawn. Historians are unsure how the events unfolded. Did both men intend to miss? Did both men intend to the kill the other, and only one did so? We can not be sure.
My interpretation (though admitted a bit speculative) is that Hamilton did not intend to fire his pistol. He cautioned his friend to careful with the weapon as he was rowed back across river as he thought it was still loaded and not discharged. Burr told friends bef0re the duel that he did not intend to let Hamilton kill him. My thought is that Burr fired first, Hamilton had raised aimed his pistol over Burr which accounts for the bullet hitting a tree branch behind Burr. The hair trigger of the Hamilton’s pistol caused it to discharge when he was hit by Burr’s shot.
Only one thing is certain, namely the result of the duel on July 11th 1804 was that Burr’s shot struck Hamilton who later died. The theater play “Hamilton” concludes with the song: “Who Lives, Who Dies, Who Tells Your Story.”