Three modes of Avraham's prayer

ברש"י ויגש אברהם לפיוס ולמלחמה ולתפלה.

In Rashi: "And Avraham drew near" — for appeasement (piyus), for war, and for tefillah (prayer) (Rashi, Bereishis 18:23).

Rashi explains that Avraham's "drawing near" to plead for Sedom embraced three modes: appeasing, doing battle, and praying.

לכאורה היינו פיוס היינו תפלה.

At first glance, appeasement and tefillah are the same thing.

It seems redundant to list both "appeasement" and "prayer," since prayer would appear to be a form of appeasing.

אך הם רמז הג' תפלות שאבות תיקנום.

But they are an allusion to the three tefillos that the Avos instituted.

The three modes correspond to the three daily prayers established by the Avos — Shacharis, Minchah, and Maariv.

כי פיוס הוא למצוא חן וחסד כי חפץ חסד הוא.

For appeasement is to find favor and chesed, for "He desires chesed" (Michah 7:18).

"Appeasement" is the avodah of chesed — seeking to find grace and kindness before Hashem, fitting for Avraham, the man of chesed.

ותפלה הוא לעורר רחמים ואין להאריך עתה:

And tefillah is to arouse rachamim (mercy); and there is no need to elaborate further now.

"Prayer" here specifically denotes awakening Hashem's mercy — a distinct avodah from appeasement — and the author leaves the rest for the reader to develop.

Summary: Rashi's three modes of Avraham "drawing near" — appeasement, war, and prayer — are not redundant but allude to the three daily tefillos instituted by the Avos. "Appeasement" is the avodah of chesed, seeking favor before Hashem, while "prayer" is the distinct work of arousing divine rachamim.