DrakeMarshall

Hm... This is I think a somewhat broad question. I will answer it to the best of my understanding.
Bear with me, because it might take a little while for me to tie all this back to shards.
 
In the cosmere, the bit of a human being that resides in the spiritual realm is not what many would typically think of as the soul. Consciousness, and what many people are used to thinking of as the soul, are actually purely associated with the cognitive realm. The spiritual realm is the realm of investiture.
A human has several attributes that exist in the spiritual realm. These include:
      -Innate investiture. The spark of life, the ability to use allomancy, and many things beside are all investiture that is associated with a sentient being and which exists within the spiritual realm.
      -Spiritual connection. We really don't know very much about this but we know it exists.
      -Identity. We don't know too much about identity either, but we do know that identity is what controls who can access a metalmind.
      -Other bits of information including a persons age and a range of other attributes.
      -If the classification of feruchemical powers is to be trusted, we can also assume that fortune is an attribute of a person's spirit.
 
Now. In terms of investiture, I believe there are two major kinds of investiture. Innate, and kinetic.
As you may have noticed, innate investiture is listed above. It is a kind of investiture that exists in the spiritual realm and is part of a sentient being. The spark of life, the ability to use allomancy, and the nahel bond are all examples of innate investiture.
Kinetic investiture I suspect does not exist within the spiritual realm. It is inside the cognitive or physical realm, and isn't innate to an individual. Stormlight is a great example of kinetic investiture.
(As for biochromatic breath... Whether it is innate or kinetic is subject to some question, but that is a discussion for another time and probably another thread)
 
Now... So far I have only been talking about the spiritual realm with respect to humans.
But, as I understand it, shards also have things like innate investiture, connection, and identity. In fact, all sentient beings do.
Most of a shard's investiture is innate investiture, and therefore in the spiritual realm.
This is because at any given time, odds are, most of a shard's power isn't actively being used.
Like all types of energy, investiture cannot be created or destroyed. So when an allomancer burns pewter and draws on some investiture from the shard of preservation to strengthen their body, the investiture returns to preservation after being used by the allomancer. The fraction of a shard's investiture that a shard is using at a given time is almost always a very small fraction of the total power they wield.
 
Now... As splintering other shards... We don't know too much about the specifics of splintering. However, I think it is reasonable to assume that splintering is indeed something that happens in the spiritual realm. As I understand it, splintering involves taking chunks of a shard's innate investiture and scattering them, so that the shard is effectively no longer one diety, but a bunch of tiny pieces. In this shattered state, it is impossible for a single sentient being to control the entire shard, which makes a splintered shard directionless and not a threat.
 
Hopefully this explains your question. Let me know if it needs clarification.