What is the difference between these worms: Caenorhabditis elegans and Eisenia fetida?
Caenorhabditis elegans is a nematode. Eisenia fetida is an annelid. They both are lophotrochozoans (more specifically, trochozoans). 

Time of Divergence

According to Michael Lynch, there are about 41 amino-acid substitutions per site between Annelida and Nematoda. According to Lynch's data, I estimated that this difference is roughly equal 100 million years. 

Therefore, assuming the rate of molecular evolution was constant, their common ancestors lived about 100 million years ago.

Difference on Anatomy

Nematodes have pseudocoelom while annelids have eucoelom. Therefore nematodes do not have a vascular blood system. However, annelids do have one. Nematodes also lack a layer of circular muscle, which annelids have. This layer of muscle allows annelids to move by shorten and elongate their bodies.

C. elegans in particular does not have a female gender. There are only male worms and hermaphrodite worms. Only the male can fertilize other worms.

E. fetida is hermaphroditic and two of them can fertilize each other.