If deviance is behavior that violates social norms and societal rules, and criminality is behavior that breaks formal criminal laws, should deviant behavior be treated differently than criminal behavior in the criminal justice system?

Answer 1

In general, not always, society's laws and regulations are created to minimize deviant behavior. More specifically we have:

When the deviance is addressed by Law and Order, it is by definition a crime. And anyone convicted of such behavior is a criminal.

But when it's not addressed by law and order, we only have social pressures (e.g., shaming) to control it. And anyone performing such behavior is not a criminal, but they might become social outcasts.

And finally society might simply ignore the deviance as being harmless, for example, and let it go on. In this latter case, if the deviance persists long enough society might morph into accepting that ignored deviance as a norm and no longer a deviance.