R' Shimon Schwab in the Artscroll sefer "Rav Schwab on Prayer" explains this disparity.
He says that:
שים שָׁלום טובָה וּבְרָכָה. חֵן וָחֶסֶד וְרַחֲמִים. The opening phrase, beginning with שִׂים שָׁלוֹם, is a prayer for inner peace, or peace of mind, in which one is at peace with himself. This is, as we have said, the highest form of peace. We ask here for טובָה וּבְרָכָה. חֵן וָחֶסֶד וְרַחֲמִים, which are all blessings through which a person can recognize that HaKadosh Baruch Hu loves him. By receiving these blessings, he has the wonderful feeling that his soul is at peace with HaKadosh Baruch Hu.
עָלֵינוּ וְעַל כָּל יִשרָאֵל עַמֶּךָ. But we are not satisfied to merely obtain this form of peace for ourselves. Rather, we pray that HaKadosh Baruch Hu may extend this serenity and peace עָלֵינוּ, to all our loved ones and then to all of יִשרָאֵל.
בָּרְכֵנוּ אָבִינוּ כֻּלָּנוּ כְּאֶחָד בְּאור פָּנֶיךָ.
HaKadosh Baruch Hu shows us a "friendly face" when we have shalom among ourselves. But, as long as there is discord among us, HaKadosh Baruch Hu shows us an angry face.
Shalom was the precondition for the giving of the Torah to Israel.
כִּי בְאור פָּנֶיךָ נָתַתָּ לָּנוּ ה' אֱלהֵינוּ תּורַת חַיִּים. This description of the Torah as something alive conveys the idea that iwas not meant to be accepted only by individuals.
And by doing so it also enhances peace between man and man.
וְאַהֲבַת חֶסֶד. The desire to do kindness to others is a special blessing of HaKadosh Baruch Hu, and it is part of the berachah of shalom among people.
וּצְדָקָה וּבְרָכָה וְרַחֲמִים וְחַיִּים
Continuing to detail the blessings of shalom among people, we list here: tzedakah, charitable deeds to each other; berachah, each one's presence is a blessing to the other; rachamim and chaim, when one is in need, the other offers him his merciful assistance, thus anabling the one in need to continue living his life normally.
The world shalom is mentioned here a second time to add circumstances where people were angry with one another -- for good cause, or not -- and there was a "berogez", a severance of a relationship; nevertheless, the blessing of shalom makes it possible for people to forgive each other -- וְשָׁלום, and to reestablish the shalom.
That is, the first part of the prayer is on the individual ("inner peace") in order to achieve the next stage of doing mitzvos to others. That is, goodness (and good qualities) and grace (in the eyes of those that see us). Once one achieves that (which all require peace of mind), then it will come both naturally to him and as a berachah from HaKadosh Baruch Hu for doing so, that he can do tzedakah, and in turn give life to those in need.