In a dream shift or a D-Shift?
one dreams that (s)he is his/her therioside
These dreams are usualy more than plain dreams, they feel special and often very diffirent than normal dreams as the sesations are such as they would be of the animal's senses.
A Dream Shift occurs when a lycanthrope becomes a wolf or werewolf in their dreams. The change is often involuntary, which means "it just happens". Lycanthropes usually have less control over what they do in this form of shifting because, unlike Lucid Dream Shifting, they are unaware that they are dreaming. A Dream Shift still happens in a normal dream, the only exception is that the dreamer can shapeshift.
The dream shift can occur in both the lucid and non lucid states.
This is sometimes the most common form of shifting, at least, for those that can remember their dreams. This is exactly how it sounds, shifting while dreaming. It could be any of the mentioned forms of shifting here, the most common being the Physical Shift (below).
A dreamshift is simply a dream where you shift into your phenotype, or any number of animals not restricted to your phenotype. I've only had one dream where I actually shifted, but many where I started as the wolf. I consider these dreamshifts even if I didn't start as human. Dreamshifting is a good way to get closer to your other side.