There was a time in Jewish history when most of the Jews were centralized in one location even after the destructions of their holy Temples. This was in Babylon. There were other Jews in Israel and other countries however, most were in Babylon. Whenever there was a question about a law or a decree that was to be made it was decided by the large court consisting of many wise rabbis in Babylon. Their decision was to be universally accepted by all Jews. Although, there were a few exceptions such as rival rabbinical groups scattered around the Levant. However, at around the year 600 C.E. the Jewish people were scattered from Babylon to other counties because of the many wars going on. From then on there was no one universal system to decide Jewish law, decrees, and customs. Instead each area of Jews made decisions only binding for that area, hence, the difference between Ashkenazim and Sephardim.
As customs were forgotten or new situations arose the greatest Rabbis in the area of Ashkenazim or Sephardim made the decisions about the customs based on their vast knowledge of the Torah. Many of the Jewish prayers were composed before the exile. However, some parts had errors in it over time from being rewritten or reprinted. Many times instructions or titles were written next to the prayers and when it was rewritten it was erroneously included in the prayer. Some prayers were added afterwards and some prayers were reformed. A good example of a prayer that is different between Ashkenazim and Sephardim is the Birkat Hamazon (Grace after Meals). The Birkat Hamazon prayer is said after meals consisting of food made from any of the five main grains including wheat, rye, oats, spelt and barley.
The Sephardim’s third blessing is “Have mercy, O God our Lord, upon us, on Israel Your people, on Jerusalem Your city, on Mt. Zion, place of Your glory, on Your palace, on Your dwelling, on Your sanctuary, and on the great and holy Temple that Bears Your name. Our father, be our Shepherd, feed us, support us, nourish us and sustain us, and grant us quick relief from all our troubles. Do not make us depend, O God our Lord, on gifts of flesh and blood, nor upon their loans-for their gifts are small and their humiliation is great-but only on Your hand, that is full, generous, rich, and open, so we not be ashamed in this world, and not be humiliated in the World to Come. O God restore the kingdom of the house of David Your anointed one to its place, quickly in our days. Blessed are You O God, who rebuilds Jerusalem in His mercy. Amen.”
The Ashkenazim’s third blessing is “Have mercy, we beg You O God our Lord on Your people Israel, on Jerusalem, Your city, on Zion, the resting place of Your glory, on the monarchy of the House of David, Your anointed and on the great and holy House upon which your name is called. Our Lord, our Father tend us, nourish us, sustain us, support us, relieve us, and grant relief to us, O God our Lord speedily, from all our troubles. Please, O God our Lord do not make us dependent neither upon the gifts of flesh and blood nor upon their loans, but only upon Your Hand that is full, open, holy, and generous, that we not be ashamed nor be humiliated for ever and ever. Rebuild Jerusalem, the city of holiness, soon in our days. Blessed are You, O God, who rebuilds Jerusalem in His mercy. Amen.”
The third blessing of Birkat Hamazon is attributed to King David and King Solomon. The blessing talks about returning to Jerusalem and rebuilding the temple. However, this blessing would be inappropriate because they were in their heights of peace and Judaism in Jerusalem then. Therefore, the blessing that they actually composed was of a more general form and asked G-d to be able to stay in Jerusalem in piece and that the temple not be destroyed. However, after the Jews were exiled a new prayer was befitting. Therefore, the prayer was reformed over time to fit with their circumstances. However, the Sephardic and the Ashkenazic version was formed a bit differently because they lived in different areas and was not able have any consensus on its formation.