Astilla

A Splinter is a specific type of fragment of a Shard's power.

What are Splinters?

Though Brandon has not stated the complete definition of what a Splinter is, in a way they are qualitative opposites of Slivers. Whereas Slivers are people who have been influenced by Shardic power, a Splinter is a thing that has never been human. One distinguishing factor of a Splinter is that they often have an intent, separate from their Shards'. Splinters are a blend of more the spiritual and cognitive and less the physical.

Known Splinters

Examples of Splinters are Honorspren, the Divine Breath that Returned hold, which are Splinters of Endowment, and the Aons inside of Seons are Splinters of Devotion.

So there are Splinters on Roshar, Sel and Nalthis.

No Splinters on Scadrial

Lerasium and atium--despite being condensed essences of their Shards--are not Splinters, so there are no Splinters in Mistborn.

Creation

It is not clear how Splinters are formed, though it appears a Shard must actively create one. Endowment seems to be able to form them at will for Returned. Odium traveled to Sel and Splintered Devotion and Dominion. Since Odium killed Tanavast, the holder of Honor, Honor was Splintered as well.