Rav Nevenzahl shlit"a, explains the difference between the korban shlamim and korban todah (which comes under the category of shlamim, but has a several different halachic criteria) in an insightful fashion that gives us direction in our avodat Hashem.

One of the halachic differences is that a korban todah must be eaten the day it is offered until chatzot (mi'd'oraysa until alot hashachar) and nothing may be left over.  A shlamim, however, may be eaten for two days and one night. Why the time difference if essentially a todah is also a shlamim?

Rav Nevenzahl explains that the answer lies in human nature.  A korban todah is brought if a person has been miraculously saved from a terrible situation. It is the nature of man that when something out of the ordinary occurs, in the beginning he is emotionally excited, uplifted. As time goes by, the impact of the event loses its strength and slowly the excitement dies down, even in a life and death situation. The Torah wants to seize the moment when a person is at the height of his emotion.  Therefore, the korban todah is eaten on the first day that it is offered when there is a tremendous overflow of gratitude to Hashem for the miracle that happened.  On the other hand, a korban shlamim is brought from a more rational place of a person wanting to do something to be closer to Hashem. As an intellectual decision, it is not critical to preserve that first moment of excitement, for it is more constant and stable, and does not wax and wane like emotions.

Torah and tefillah, Rav Nevenzahl goes on to explain, are like the shlamim and the todah.  They are two distinct entities that together bring a person to shleimut in avodat Hashem.  The Torah (which parallels the shlamim) is intellectual, grasped by the mind.  What one has learned at a young age can stay with them for the rest of their lives. The Torah is thus referred to the part of our avodah that is "chayei olam" - eternal life. Tefillah on the other hand, is an avodah of the emotions (much like the korban todah).  Of course, one must understand the words of tefillah, but to really connect to Hashem through tefillah, one must live the words.  To feel that the words he is saying is not just a compilation composed by the Anshei Knesset Hagedolah, but that every word applies to him. In the words of Channah (Shmuel alef, 1:15) "V’eshpoch et nafshi lifnei Hashem" - tefillah is when one pours out their soul before Hashem.

May we be zocheh to truly daven and pour out our emotions to Hashem. 

Shabbat Shalom.