A Sliver is an individual who has held the power of a Shard and has since released it. A briefly held time, holding the infinite power of a Shard, but no longer does. That changes one's soul, and leaves markers on it. There is a threshold to that power where one might then be considered to be a Sliver of Adonalsium.
Being a Sliver has an influence on an individual after a Shard's power has been released. There is a residue left behind which has several effects, one of which is that an individual who is capable of recognizing Investiture would be able to look upon another and tell that that other is a Sliver.
Slivers are a topic that is frustratingly vague. The stories of men and women with insurmountable powers, or who held them at one point, are deceptively plentiful among the cosmere, yet lack the details or verification necessary to form meaningful conclusions.
It seems that power alone does not make someone a Sliver. Investiture may be a part of it, but if there is a point where a physical being can accumulate enough Investiture in order to become a Sliver, it isn't known. Yet in the few documented cases that are have accounted for in The Words of Founding, readers still don't get a clear picture of what exactly makes a Sliver.
With regard to the Lord Ruler, he wielded a great power when he reached the Well of Ascension. This power let him shape the world according to his will. The Lord Ruler created life, and altered people without them even knowing what had happened. He touched the power of a Shard and came out the other side a changed man. After this event he called himself the Sliver of Infinity. This might have been just an ego title fueled by his hubris, but his example sets a good precedent for what a Sliver is. So, this is a reference point.
The Well of Ascension, however, was not just a collection of Investiture. It was a Shardpool, which is to say it was a part of a Shard's body. Body is the traditional term, but it's more like the power and Essence of a Shard, which is far more than just Investiture. When someone takes in Investiture - pure Investiture - s/he receives power. From the accounts of the Ascended Warrior, readers learned that the Power of the Well wasn't just Investiture; it was knowledge, mind expansion, and capacity to use that Investiture beyond the confines of human capabilities. The actions performed by the Lord Ruler had no resemblance to Allomancy, Feruchemy or Hemalurgy. He learned of these arts intimately, but it was not by their power that he moved mountains. This power is far greater in scope and is not limited to the metallic arts.
To exemplify the distinction between a Sliver and a highly invested individual, after the Many War, the God Kings of Halandrin carried and passed on an incredible collection of Bio-Chromatic Breath. Breath is a form of innate Investiture found in each individual on Nalthis. These individuals can give this Breath to another, and the collection of Breath in a person increases each their capacity and physical abilities. Hold enough breath and one can extend one's life, or awaken inanimate objects, giving them temporary life. The God King holds tens of thousands of Breaths. However, this does not necessarily make him a Sliver. This Breath is so immense that it is unclear as to which specific powers he has access. However, this power derives from Investiture that is natural, but the Breath does not grant knowledge or powers of creation. The powers of the God King are immense, but they still follow the order of Awakening, and do not allow him to alter the planet itself. The Breath does seem to impart powerful knowledge of Awakening instinctively at this level, but this is still not an expansion of the mind, but more a heightened awareness of things known to the subconscious.
So, the God King is not a Sliver. Yet there is something mysterious about the origins of the Returned. The Returned of Nalthis, the spren of Roshar, and the seons of Elantris seem to share common elements. However, these things still are not Slivers.
A Sliver is a person who held the power of a Shard, but gave up or lost the power, leaving them deflated. Likely, this caused a permanent change in the individual, but how this change would manifest in the abilities of the Lord Ruler cannot be determined.
There is little to be learned about Slivers at the moment. Perhaps someday readers will see and account for more Slivers. For now, Splinters are quite fascinating, especially when the similarities that exist between Splinters and Hemalurgic spikes are examined.
- Paraphrased from transcript.