Prior to calling the Kohen aliyah for Torah reading, there is an introductory paragraph said by the gabbai or ba'al kri'ah. Following is Nusach Ashkenaz as found in Art Scroll and Birnbaum, Ashkenaz, among others.
During weekday and Shabbat afternoon readings it begins with
ותגלה ותראה עלינו בזמן קרוב
On Shabbat and Yom Tov Shacharit, the paragraph begins
ויעזור ויגן ויושיע
I initially thought that the reason that the Shabbat paragraph was shorter is related to the general "concept" that we avoid making requests on Shabbat. However, both paragraphs look like a formulation of a request.
Why are there two different versions? Is there something special conveyed by these versions that makes one more appropriate for weekday or Shabbat / Yom Tov?
Related to this, if Shabbat is "special" in some way, then why do we revert to the weekday format for Shabbat mincha? Is the reason related more to the "type" of reading, i.e. Shabbat mincha reading is identical to the reading the rest of the week? (except for next week :-0)