Let us preface with a fundamental distinction between the epistle and its elucidation:
The epistle emphasizes mainly the tzaddik’s legacy — “He has left life for all the living.” The tzaddik imbues “life” (also after his passing) into the avodah of “every person commensurate with the degree of the person’s bond {to the tzaddik},” and also “in worldly matters..., for the righteous protect the world.”
Conversely, the main emphasis in the “elucidation” is on the disciple receiving — how disciples continue to benefit from the tzaddik’s avodah even after their mentor dies. (Moreover, not only do they enjoy a ray {of the tzaddik’s spirit} but they partake “from the essence of their master’s spirit”).
On this basis, we can proffer a possible difference between the epistle and the elucidation mentioned above:
The word “act” {הָעוּלְפּ} connotes that the energy expended through “acting” and invested in the “act” is now detached from the person who performed the act. (We can posit that the degree of detachment {between the energy and the person} is more profound than {when a person’s energy is expended} in a “deed.”) Therefore, it makes sense that the identity of the person who performed the act is indiscernible in the act itself.
Accordingly, when discussing the disciples receiving, the wording employed is “his speech and thoughts” (through which the tzaddik’s emotional attributes — his love, fear, and faith — radiate openly).
In contrast, when the Alter Rebbe wants to demonstrate the greatness of the tzaddik and what he accomplishes, the Alter Rebbe emphasizes that the tzaddik’s primary virtue lies in “the act he performed.” This is because the tzaddik’s essence is expressed (not so much in the aspects and effects of his avodah in which the virtue of his avodah is discerned, but rather) specifically in his (external) acts.
(This is similar to what was discussed earlier regarding mitzvos, where the Essential Will of mitzvos is expressed primarily in the actual mitzvah deed.)
