It appears you want to give different names to old ideas. Perhaps you think that changes them.
You keep describing punishment, and pretending it is something different.
Have a great day, God Bless.
A sentence for the purpose of retribution (punishment) may look the same as a sentence with the purpose of restraint and protection, like imprisonment. But you should be able to see that the difference in the reasons and goals for incarceration will be clearly seen in the different methods and approaches of how the whole "Dept of Corrections" is set up and the means by which the sentence is carried out and implemented.
For example, today, "punishment" means that a dangerous criminal is let go because he's "done his time." There is ofttimes relatively little concern for the safety of society or victims, restitution, or rehabilitation. That makes sense because those were not the reasons for incarceration in the first place. But under sentencing for the express purpose of restraint and protection of society and restitution, the priority would be keeping society safe, repaying the victim where possible and reasonable, and verifiable rehab.