What exactly is meant by “self”, considering there is more to our being than just our everyday mundane self?

This is a matter of semantics, so we have to clear up the definitions. The key to solving this is that technically there are at least three selves: 1) the Higher Self (of which you are an independent and self-aware projection), 2) the middle self (you reading this now), and 3) the baser self (also known as the “shadow”, which Jung calls the “id”, Castaneda the “predator”, and generally speaking is the sum total of your biological and social programming, negative entity attachments, and negative subconscious complexes).

When talking about the Higher Self and lower self, the definition of “lower self” depends on what it’s relative toward. If it’s you compared to your Higher Self, then you are technically its lower self. But the baser self is lower than even you. So the phrase “I will not give in to my lower self” is said from the middle self regarding the baser self, while “the lower self must align with the Higher Self” is said from the middle relative to the higher.

Further, the ego in the original Jung/Freudian sense simply means “the me” which would mean your middle self, a.k.a. you. However, when we say that someone is being egotistical, or that we must conquer the ego, we’re really talking about the baser self being overactive and needing to be reigned in. So “ego” can mean either the middle or baser self, depending on context.

So when STO (Service to Others) and STS (Service to Self) refer to self and other, this “self” refers mainly to the middle self, the one that is incarnate, consciously thinking, acting, choosing, and growing as an individual.

This middle self has the option of choosing in favor of the Higher Self or the baser self, typically stated as choosing between spirit or ego. Ego in that context means the baser self, the “other, within” — basically the devil on your shoulder. You can’t serve the baser self by serving others. You can only serve your middle and Higher Self by serving others, because only these get anything out of that. The baser self is strictly a predatory/parasitic/mechanical thing and the source of Service to Self impulses.