There are two differences of note between the 3 Nephi verses and those in Matthew. The first, in verse 33, in 3 Nephi, is the continued New World emphasis on the written commandment, where Matthew speaks of the oral law.
The second is Matthew 5:35: “Nor by the earth; for it is his footstool: neither by Jerusalem; for it is the city of the great King.” In 3 Nephi, the phrase “neither by Jerusalem; for it is the city of the great King” is left out. That would make sense, since the New World Jerusalem was a city infamous for apostate Nephites who would not hear the sons of Mosiah (see Alma 21:1–4).
These verses deal with the more ancient custom of declaring oaths. Prior to the concept of written contracts, oaths were used to officially seal agreements. What had happened by Jesus’s time was that different oaths might have different meanings, some being stronger than others.
What Jesus is teaching is that we should be honest in our dealings with others. We should not create loopholes in our agreements that would allow us to break our agreement easily. Thus, we say “yea, yea; nay, nay.” In other words, we say what we mean, without so many nuances that we could not be trusted.