What is the difference between offset and silkscreen CD?

Silkscreen and offset printing are the method of printing for large run CD/DVD replication. Is one better than the other? That depends on the artwork. See the 2 examples here:

The one on the left is offset and the one on the right is silkscreen. Offset printing is best used on photographic images and any artwork that does not have areas of solid colors. Offset printing gives photos a detailed and realistic look.

On the other hand, silkscreen is best for solid colors such as the example here. The colors are vibrant and consistent throughout. For setting up artwork for silkscreening you need to use Pantone colors (or sometimes called PMS colors) and vector art is preferred.