The same way an email is way less formal than a written letter or those rare SMSes from relatives that come full with salutation and signature.
Heck, even in a forum like this one: we don't add the salutation nor signature, but in an email we would.
Context matters a lot and the ability to adjust the message to match the context is also part of communication skill.
The reason why I believe that chat is different from mail or a forum post is that chat messages cause your phone to make sounds and/or vibrate. They are shown on your home screen where they also will share the screen estate with other people's messages. Shorter messages are more useful.