I think this sutta is an interesting contrast to the prior MN37, which is the “shorter discourse”, and is given to a deva who is a stream-attainer. There, the deva is lightly admonished for being distracted by sense pleasures. In MN38, though, Sati, the fisherman’s son, is strongly scolded for having the wrong view that a self consciousness moves from one life to the next in a stable/identical form.
This sutta also lays out dependent origination, which is a central concept in Buddhism. It is very appropriate that dependent origination is described here because that is the answer to the question of what moves from one life to the next–there is no atman (self), instead, there is a “process”, that of dependent origination, which is conditioned by what happened previously (on an incredibly complex level; the Buddha mentions this in DN15). In my daily life, it is helpful to try to remind myself that each decision I make is shaping the “process” of my experience, and that if I want to be happy in the future, I need to make skillful/healthy choices in this moment. The choices/actions I make now, if they are wise/skillful, become a “gift” to my future being.
The analogy of a flame being transmitted from one stick to another is sometimes used to refer to this awareness, however, to my understanding, the Buddha did not explicitly state this. For example, Nagasena mentioned it his discussions with King Milinda (An Explanation of Rebirth)
Another point raised in this sutta is the concept of relishing/enjoying feelings: “Being so full of favoring and opposing, when they experience any kind of feeling—pleasant, unpleasant, or neutral—they approve, welcome, and keep clinging to it. This gives rise to relishing. Relishing feelings is grasping. Their grasping is a requirement for continued existence.” It is helpful to contrast this, though, to the non-attached enjoyment that an arahant may experience, which also describe “delighting” in an experience; in Theragatha 18, Mahakassapa says:
“Spread with garlands of vines, places delighting the mind, resounding with elephants, appealing: those rocky crags refresh me."
I also thought it was interesting that the sutta ends with Buddha saying that the mendicant Sāti, the fisherman’s son, “is caught in a vast net of craving, a tangle of craving”–that is a lovely example of the Buddha’s gift for metaphors and engaging characters—a fisherman like Sati works with a net, and the metaphor of a net for craving helps link these different elements together in the sutta.