A man, A Soul, Nefesh Adam
The Torah starts off describing the sacrificial system by saying “Adam ki Yakriv.” A man (a person, it includes all sexes) who brings a sacrifice. Later on, when talking about a meal offering and then a sin offering, it says “Nefesh Ki Yakriv.” A soul who sacrifices. What is the difference between Adam and Nefesh?
There is a debate elsewhere in the Talmud about whether Adam is used of all humanity or only of Israelites. In the Ethics of The Fathers, part of the Mishna, the question is raised as to whether God cares only about Jews or humanity. And the overwhelming body of opinion there agrees that God cares about all human beings, all his creation.
And that is why one opinion says that as the law allows anyone, no matter where they come from or who they are, may bring a sacrifice if it is genuinely offered to God. And that the different usage of words to describe human beings reflects this point. No matter whether you are a person or a soul you are a child of God and may approach Him through the sacrificial system.
Another opinion says this distinction is a different one. Anyone brings sacrifices as a human being regardless of status or identity. When it comes to the actual sacrifices certain ones are like meal offerings are designed for the poor. To give them a feeling of importance and values. We are told in the Torah to “know the soul (nefesh) of the stranger and the poor.” So, when the poor bring sacrifices they come as suffering souls.
But others who suffer are those who have sinned and regret it. They regret it because their souls have overcome the physical appetites and urges. They too are souls in pain.
This is a simple illustration of how rabbinic interpretation likes to focus on differences of language and style to draw some important moral lesson out of the text. Rather than just assume it is a scribal oversight or indication of different authors.