Why does Vardaman call his mother a fish, and Darl call her a horse?

One of Faulkner's themes in "As I Lay Dying" is that of identity.  Vardamen, the baby of the family, seeks to identify himself in relation to other members of his family.  He repeats these identifications saying repeatedly, "Darl is my brother" and "My mother is a fish."  After he catches a a big fish and Anse cooks it, Vardamen begins to confuse the big fish with his mother.  When Pa tells Jewel to leave the horse because that will all go in the wagon, Vardamen remarks,

But my mother is a fish. Vernon seen it.  He was there.

'Jewel's mother is a horse,' Darl said.

Then mine can be fish, cant it, Darl? I said.

Jewel is my brother.

Then mine will have to be a horse, too.' I said.

Later, in one of his chapters Vardamen relates how the flooded waters cause the mules to drown and the coffin of his mother to get away from the family in the water.  Darl comes out of the water empty-handed.  Vardamen believes that Darl will catch the casket, but this does not happen:

Where is ma, Darl? I said. 'You never got her.  You knew she is a fish but you let her get away.  You never got her.  Darl. Darl. Darl.'

Vardeman continues in his desire to pursue meanings in words.  Sadly, for Vardeman the process of identification is not fulfilled as he repeats "My mother is a fish" and "Darl is my brother."  On the other hand Darl's attempts at identification prove more disturbing as he evokes existential questions, questions of the essence of human consciousness:

I don't know what I am.  I don't know if I am or not. Jewel knows that he is because he does not know that he does not know whether he is or not.