Weres do exist; however, they do NOT assume an animal's form on every full moon. They do shift or shape shift in a fashion but it is not physically.
You no more become a were by being bitten than you can become a vampire by being fed on or by drinking our blood, that is a myth.
Aura-shifting is changing your basic energy/ animus which is a part of every living thing. This change may be genuine, or cosmetic, the difference is totally irrelevant since both accomplish the same goal. There have been cases of using mirrors to gain a fuller effect of aura-shifting, seeing ones face and head change.
Seeing an aura isn't a set procedure. Therefore, most aura-shifts are "felt" rather than seen.
Dream shifting is simply shifting in your dreams, whether it be lucid dreaming or not.
Mental-shifting is a oneness with your totem animal, spirit guide, or power animal, that goes way beyond the normal relationship of the state of your mind, being, spirit, brought about either by intent or accident. It is accompanied with an intensity of your normal senses to an extent not normally seen in everyday life.
The intensity, duration, and effects of this shift vary from person to person, and no doubt from shift to shift, assuming it is not just a one time occurance. This might best be described as loosing yourself in your animal nature for a while, until the threat is over or your instincts no longer have something to react to (like running in the moonlight).
By shifting, you lose part of your humanity for a time, and let your animal instincts take over to some degree (the degree varies by the seriousness of the threat). The mental processes rework themselves to such a high degree that sensory inputs are changed, causing visual or aural distortions (in some cases others will sense or see the change especially if they are psychic [awakened humans]).
If strong enough, you could feel some sort of displacement of your body, or parts of it. Often felt is a strong bond with your animal while shifted into its form. This may be due to your particular animal's nature being "close to the surface" as the case may be.
Where does the animal come from? Theories include reincarnation soul migration where one is "remembering" a previous lifetime of having been a wolf.
Transspeciation, not unlike a transgender situations where someone was born into a body with the wrong soul. Human body wolf soul.
Misincarnation where you are born into the wrong body altogether (meant to be onething [like a wolf], but born as another [like a human]).
Spirit shift is a shift in mentality or form which takes place and is what is known as a vision quest, journey, or an out of body event (astral travel/jolting).