(Please forgive the delay in response. Technical problems prevented the mailing of a number of responses.)

Since the title of this question is Shabbos 002, I am assuming that the issue is why did the Rambam in Mishneh Torah, when he cited the Din of the Mishnah (see Rambam, Hilchos Shabbat 12:9, 13:2, and 13:7) not mention anything about the poor and rich person described by the Mishnah?

1) This question is asked by the Aruch la'Ner in Sukah (43b, DH Mipnei). He notes that it is well-known that it is not the way of the Rambam to change the phrases used in the Mishnah and Beraisa when he summarises them in his Mishnah Torah, so we have to understand why the Rambam changed this detail of the Mishnah.

2) The Aruch la'Ner strengthens his question by citing the Bartenura on the Mishnah, who writes that there indeed is a special reason for why the Mishnah mentions the fact that a poor and rich man are involved in the Mishnah; namely, that the Mishnah is telling us that even though the rich man is doing a Mitzvah of giving charity when he gives the pauper a present of a loaf of bread, nevertheless this is considered a "Mitzvah ha'Ba'ah b'Aveirah" -- a Mitzvah that comes about through a transgression -- and not only is this forbidden, but he also is liable to bring a Korban Chatas to atone for his inadvertent sin. Therefore, the Aruch la'Ner asks, since there is a good reason for why the Mishnah gives its example of the Melachah in the form of the pauper and the rich man, why did the Rambam omit this detail?

3) The Aruch la'Ner answers that the Rambam's intention here is to answer the question of the Tosfos Yom Tov on the Bartenura: why indeed is the rich man liable when he gives the loaf to the pauper? We should say that he is exempt because he was thereby performing a Mitzvah? The Aruch la'Ner answers this by asserting that the Rambam maintains that the Halachah does not follow the Mishnah on 2a, because the Mishnah maintains that if someone errs when doing a Mitzvah and does a Mitzvah at the same time as a transgression, he is liable to bring a Korban Chatas. The Rambam, however, maintains that if someone did a Mitzvah and at the same time did an Aveirah, he is exempt from a Korban (Hichos Shegagos 2:8). Therefore, the Rambam would maintain that if the rich man passed the loaf from Reshus ha'Rabim to the pauper in Reshus ha'Yachid, he would be exempt because he did a Mitzvah in so doing, even though this also involved a transgression. Therefore, the Rambam omitted the detail of the poor and the rich when he cited the law of the Mishnah -- because he wanted to illustrate a case which would involve liability to bring a Korban.

(A source for the Rambam's ruling is the Gemara in Shabbos 137a, that if there were two babies, one which had to have his Bris Milah on Shabbos and the other on Sunday, and the Mohel forgot and did the Bris for the Sunday baby on Shabbos, according to Rebbi Yehoshua he is exempt. The Halachah follows the view of Rebbi Yehoshua.)

4) I later posed your question to a Gadol. He replied that the reason why the Rambam did not mention the fact that a poor and rich person are involved in the carrying in and out is that there is no Nafka Minah that emerges from this fact.

We can learn from this that the Rambam often does not mention in the Mishnah Torah details mentioned in the Gemara that make no difference to the Halachah.

B'Hatzlachah Rabah,

Dovid Bloom

I posed the above question to a Gadol and he replied that the reason the Rambam did not mention the fact that a poor and rich person are involved in the carrying in and out, is because there is no Nafka Mina that emerges from this fact.

We can learn from this that the Rambam often does not mention in Mishneh Torah, details mentioned in the Gemara that make no difference to the Halacha.

Dovid Bloom

1) It is true that I did use the word "rich" to describe the person giving the item to the pauper (and in fact the Bartenura also calls him a rich man). However, I think that we should say that the person giving the donation to the poor person is not necessarily literally rich. One does not have to be rich to give charity. The Mishnah actually refers to him as "Ba'al ha'Bayis," a householder. Anyone who is not homeless can give Tzedakah.

2) Therefore, even though we might expect a genuinely rich person to live in a house which is withdrawn from the main street with his own private grounds, the Mishnah is not necessarily discussing such a wealthy person. Since the Mishnah might be referring to a person of average means, it is quite possible that his house is immediately adjacent to Reshus ha'Rabim. It is this person of average means whom the Mishnah describes as distributing charity.

Kol Tuv,

Dovid Bloom