Bequeathed Lord Soul Shards differ from Lord Souls in that they are shards of a "great soul" (presumably Gwyn's own soul). The owners of these shards were awarded them because Gwyn recognized the talent of the Four Kings of New Londo as leaders (before they fell to the Dark), and because Seath aided the Lords in the war of the Dragons.
Soul of one of the Four Kings, who fell to the Dark. A fragment of a Lord Soul discovered at the dawn of the Age of Fire.
Lord Gwyn recognized the foresight of these four great leaders of New Londo, and granted them their ranks and the fragments of a great soul. Although this is not a full Lord Soul, it can still satiate the Lordvessel.
Soul of the albino dragon, Seath the Scaleless. A fragment of a Lord Soul discovered at the dawn of the Age of Fire.
Seath allied with Lord Gwyn and turned upon the dragons; for this he was awarded Dukedom embraced by the royalty, and given a fragment of a great soul. Although just a piece, it will still satiate the Lordvessel.